diff --git a/README.md b/README.md
index 8f442e212..295ca96db 100644
--- a/README.md
+++ b/README.md
@@ -25,6 +25,7 @@
 - [Categorical DQN (C51)](https://arxiv.org/pdf/1707.06887.pdf)
 - [Quantile Regression DQN (QRDQN)](https://arxiv.org/pdf/1710.10044.pdf)
 - [Implicit Quantile Network (IQN)](https://arxiv.org/pdf/1806.06923.pdf)
+- [Fully-parameterized Quantile Function (FQF)](https://arxiv.org/pdf/1911.02140.pdf)
 - [Policy Gradient (PG)](https://papers.nips.cc/paper/1713-policy-gradient-methods-for-reinforcement-learning-with-function-approximation.pdf)
 - [Natural Policy Gradient (NPG)](https://proceedings.neurips.cc/paper/2001/file/4b86abe48d358ecf194c56c69108433e-Paper.pdf)
 - [Advantage Actor-Critic (A2C)](https://openai.com/blog/baselines-acktr-a2c/)
diff --git a/docs/api/tianshou.policy.rst b/docs/api/tianshou.policy.rst
index d8579435c..39f478ca5 100644
--- a/docs/api/tianshou.policy.rst
+++ b/docs/api/tianshou.policy.rst
@@ -40,6 +40,11 @@ DQN Family
    :undoc-members:
    :show-inheritance:
 
+.. autoclass:: tianshou.policy.FQFPolicy
+   :members:
+   :undoc-members:
+   :show-inheritance:
+
 On-policy
 ~~~~~~~~~
 
diff --git a/docs/index.rst b/docs/index.rst
index 87189fd5f..4afe03aa8 100644
--- a/docs/index.rst
+++ b/docs/index.rst
@@ -15,6 +15,7 @@ Welcome to Tianshou!
 * :class:`~tianshou.policy.C51Policy` `Categorical DQN <https://arxiv.org/pdf/1707.06887.pdf>`_
 * :class:`~tianshou.policy.QRDQNPolicy` `Quantile Regression DQN <https://arxiv.org/pdf/1710.10044.pdf>`_
 * :class:`~tianshou.policy.IQNPolicy` `Implicit Quantile Network <https://arxiv.org/pdf/1806.06923.pdf>`_
+* :class:`~tianshou.policy.FQFPolicy` `Fully-parameterized Quantile Function <https://arxiv.org/pdf/1911.02140.pdf>`_
 * :class:`~tianshou.policy.PGPolicy` `Policy Gradient <https://papers.nips.cc/paper/1713-policy-gradient-methods-for-reinforcement-learning-with-function-approximation.pdf>`_
 * :class:`~tianshou.policy.NPGPolicy` `Natural Policy Gradient <https://proceedings.neurips.cc/paper/2001/file/4b86abe48d358ecf194c56c69108433e-Paper.pdf>`_
 * :class:`~tianshou.policy.A2CPolicy` `Advantage Actor-Critic <https://openai.com/blog/baselines-acktr-a2c/>`_
diff --git a/examples/atari/README.md b/examples/atari/README.md
index 971231b65..a46fcac5c 100644
--- a/examples/atari/README.md
+++ b/examples/atari/README.md
@@ -68,6 +68,20 @@ One epoch here is equal to 100,000 env step, 100 epochs stand for 10M.
 | SeaquestNoFrameskip-v4      | 4874        | ![](results/iqn/Seaquest_rew.png)     | `python3 atari_iqn.py --task "SeaquestNoFrameskip-v4"`  |
 | SpaceInvadersNoFrameskip-v4 | 1498.5      | ![](results/iqn/SpaceInvaders_rew.png) | `python3 atari_iqn.py --task "SpaceInvadersNoFrameskip-v4"`  |
 
+# FQF (single run)
+
+One epoch here is equal to 100,000 env step, 100 epochs stand for 10M.
+
+| task                        | best reward | reward curve                          | parameters                                                   |
+| --------------------------- | ----------- | ------------------------------------- | ------------------------------------------------------------ |
+| PongNoFrameskip-v4          | 20.7        | ![](results/fqf/Pong_rew.png)         | `python3 atari_fqf.py --task "PongNoFrameskip-v4" --batch-size 64` |
+| BreakoutNoFrameskip-v4      | 517.3       | ![](results/fqf/Breakout_rew.png)     | `python3 atari_fqf.py --task "BreakoutNoFrameskip-v4" --n-step 1` |
+| EnduroNoFrameskip-v4        | 2240.5      | ![](results/fqf/Enduro_rew.png)       | `python3 atari_fqf.py --task "EnduroNoFrameskip-v4"`  |
+| QbertNoFrameskip-v4         | 16172.5     | ![](results/fqf/Qbert_rew.png)        | `python3 atari_fqf.py --task "QbertNoFrameskip-v4"`  |
+| MsPacmanNoFrameskip-v4      | 2429        | ![](results/fqf/MsPacman_rew.png)     | `python3 atari_fqf.py --task "MsPacmanNoFrameskip-v4"`  |
+| SeaquestNoFrameskip-v4      | 10775       | ![](results/fqf/Seaquest_rew.png)     | `python3 atari_fqf.py --task "SeaquestNoFrameskip-v4"`  |
+| SpaceInvadersNoFrameskip-v4 | 2482        | ![](results/fqf/SpaceInvaders_rew.png) | `python3 atari_fqf.py --task "SpaceInvadersNoFrameskip-v4"`  |
+
 # BCQ
 
 To running BCQ algorithm on Atari, you need to do the following things:
diff --git a/examples/atari/atari_fqf.py b/examples/atari/atari_fqf.py
new file mode 100644
index 000000000..110a57167
--- /dev/null
+++ b/examples/atari/atari_fqf.py
@@ -0,0 +1,186 @@
+import os
+import torch
+import pprint
+import argparse
+import numpy as np
+from torch.utils.tensorboard import SummaryWriter
+
+from tianshou.policy import FQFPolicy
+from tianshou.utils import BasicLogger
+from tianshou.env import SubprocVectorEnv
+from tianshou.trainer import offpolicy_trainer
+from tianshou.data import Collector, VectorReplayBuffer
+from tianshou.utils.net.discrete import FractionProposalNetwork, FullQuantileFunction
+
+from atari_network import DQN
+from atari_wrapper import wrap_deepmind
+
+
+def get_args():
+    parser = argparse.ArgumentParser()
+    parser.add_argument('--task', type=str, default='PongNoFrameskip-v4')
+    parser.add_argument('--seed', type=int, default=3128)
+    parser.add_argument('--eps-test', type=float, default=0.005)
+    parser.add_argument('--eps-train', type=float, default=1.)
+    parser.add_argument('--eps-train-final', type=float, default=0.05)
+    parser.add_argument('--buffer-size', type=int, default=100000)
+    parser.add_argument('--lr', type=float, default=5e-5)
+    parser.add_argument('--fraction-lr', type=float, default=2.5e-9)
+    parser.add_argument('--gamma', type=float, default=0.99)
+    parser.add_argument('--num-fractions', type=int, default=32)
+    parser.add_argument('--num-cosines', type=int, default=64)
+    parser.add_argument('--ent-coef', type=float, default=10.)
+    parser.add_argument('--hidden-sizes', type=int, nargs='*', default=[512])
+    parser.add_argument('--n-step', type=int, default=3)
+    parser.add_argument('--target-update-freq', type=int, default=500)
+    parser.add_argument('--epoch', type=int, default=100)
+    parser.add_argument('--step-per-epoch', type=int, default=100000)
+    parser.add_argument('--step-per-collect', type=int, default=10)
+    parser.add_argument('--update-per-step', type=float, default=0.1)
+    parser.add_argument('--batch-size', type=int, default=32)
+    parser.add_argument('--training-num', type=int, default=10)
+    parser.add_argument('--test-num', type=int, default=10)
+    parser.add_argument('--logdir', type=str, default='log')
+    parser.add_argument('--render', type=float, default=0.)
+    parser.add_argument(
+        '--device', type=str,
+        default='cuda' if torch.cuda.is_available() else 'cpu')
+    parser.add_argument('--frames-stack', type=int, default=4)
+    parser.add_argument('--resume-path', type=str, default=None)
+    parser.add_argument('--watch', default=False, action='store_true',
+                        help='watch the play of pre-trained policy only')
+    parser.add_argument('--save-buffer-name', type=str, default=None)
+    return parser.parse_args()
+
+
+def make_atari_env(args):
+    return wrap_deepmind(args.task, frame_stack=args.frames_stack)
+
+
+def make_atari_env_watch(args):
+    return wrap_deepmind(args.task, frame_stack=args.frames_stack,
+                         episode_life=False, clip_rewards=False)
+
+
+def test_fqf(args=get_args()):
+    env = make_atari_env(args)
+    args.state_shape = env.observation_space.shape or env.observation_space.n
+    args.action_shape = env.action_space.shape or env.action_space.n
+    # should be N_FRAMES x H x W
+    print("Observations shape:", args.state_shape)
+    print("Actions shape:", args.action_shape)
+    # make environments
+    train_envs = SubprocVectorEnv([lambda: make_atari_env(args)
+                                   for _ in range(args.training_num)])
+    test_envs = SubprocVectorEnv([lambda: make_atari_env_watch(args)
+                                  for _ in range(args.test_num)])
+    # seed
+    np.random.seed(args.seed)
+    torch.manual_seed(args.seed)
+    train_envs.seed(args.seed)
+    test_envs.seed(args.seed)
+    # define model
+    feature_net = DQN(*args.state_shape, args.action_shape, args.device,
+                      features_only=True)
+    net = FullQuantileFunction(
+        feature_net, args.action_shape, args.hidden_sizes,
+        args.num_cosines, device=args.device
+    ).to(args.device)
+    optim = torch.optim.Adam(net.parameters(), lr=args.lr)
+    fraction_net = FractionProposalNetwork(args.num_fractions, net.input_dim)
+    fraction_optim = torch.optim.RMSprop(fraction_net.parameters(),
+                                         lr=args.fraction_lr)
+    # define policy
+    policy = FQFPolicy(
+        net, optim, fraction_net, fraction_optim,
+        args.gamma, args.num_fractions, args.ent_coef, args.n_step,
+        target_update_freq=args.target_update_freq
+    ).to(args.device)
+    # load a previous policy
+    if args.resume_path:
+        policy.load_state_dict(torch.load(args.resume_path, map_location=args.device))
+        print("Loaded agent from: ", args.resume_path)
+    # replay buffer: `save_last_obs` and `stack_num` can be removed together
+    # when you have enough RAM
+    buffer = VectorReplayBuffer(
+        args.buffer_size, buffer_num=len(train_envs),
+        ignore_obs_next=True, save_only_last_obs=True, stack_num=args.frames_stack)
+    # collector
+    train_collector = Collector(policy, train_envs, buffer, exploration_noise=True)
+    test_collector = Collector(policy, test_envs, exploration_noise=True)
+    # log
+    log_path = os.path.join(args.logdir, args.task, 'fqf')
+    writer = SummaryWriter(log_path)
+    writer.add_text("args", str(args))
+    logger = BasicLogger(writer)
+
+    def save_fn(policy):
+        torch.save(policy.state_dict(), os.path.join(log_path, 'policy.pth'))
+
+    def stop_fn(mean_rewards):
+        if env.spec.reward_threshold:
+            return mean_rewards >= env.spec.reward_threshold
+        elif 'Pong' in args.task:
+            return mean_rewards >= 20
+        else:
+            return False
+
+    def train_fn(epoch, env_step):
+        # nature DQN setting, linear decay in the first 1M steps
+        if env_step <= 1e6:
+            eps = args.eps_train - env_step / 1e6 * \
+                (args.eps_train - args.eps_train_final)
+        else:
+            eps = args.eps_train_final
+        policy.set_eps(eps)
+        logger.write('train/eps', env_step, eps)
+
+    def test_fn(epoch, env_step):
+        policy.set_eps(args.eps_test)
+
+    # watch agent's performance
+    def watch():
+        print("Setup test envs ...")
+        policy.eval()
+        policy.set_eps(args.eps_test)
+        test_envs.seed(args.seed)
+        if args.save_buffer_name:
+            print(f"Generate buffer with size {args.buffer_size}")
+            buffer = VectorReplayBuffer(
+                args.buffer_size, buffer_num=len(test_envs),
+                ignore_obs_next=True, save_only_last_obs=True,
+                stack_num=args.frames_stack)
+            collector = Collector(policy, test_envs, buffer,
+                                  exploration_noise=True)
+            result = collector.collect(n_step=args.buffer_size)
+            print(f"Save buffer into {args.save_buffer_name}")
+            # Unfortunately, pickle will cause oom with 1M buffer size
+            buffer.save_hdf5(args.save_buffer_name)
+        else:
+            print("Testing agent ...")
+            test_collector.reset()
+            result = test_collector.collect(n_episode=args.test_num,
+                                            render=args.render)
+        rew = result["rews"].mean()
+        print(f'Mean reward (over {result["n/ep"]} episodes): {rew}')
+
+    if args.watch:
+        watch()
+        exit(0)
+
+    # test train_collector and start filling replay buffer
+    train_collector.collect(n_step=args.batch_size * args.training_num)
+    # trainer
+    result = offpolicy_trainer(
+        policy, train_collector, test_collector, args.epoch,
+        args.step_per_epoch, args.step_per_collect, args.test_num,
+        args.batch_size, train_fn=train_fn, test_fn=test_fn,
+        stop_fn=stop_fn, save_fn=save_fn, logger=logger,
+        update_per_step=args.update_per_step, test_in_train=False)
+
+    pprint.pprint(result)
+    watch()
+
+
+if __name__ == '__main__':
+    test_fqf(get_args())
diff --git a/examples/atari/results/fqf/Breakout_rew.png b/examples/atari/results/fqf/Breakout_rew.png
new file mode 100644
index 000000000..409a2adf5
Binary files /dev/null and b/examples/atari/results/fqf/Breakout_rew.png differ
diff --git a/examples/atari/results/fqf/Enduro_rew.png b/examples/atari/results/fqf/Enduro_rew.png
new file mode 100644
index 000000000..3d5125983
Binary files /dev/null and b/examples/atari/results/fqf/Enduro_rew.png differ
diff --git a/examples/atari/results/fqf/MsPacman_rew.png b/examples/atari/results/fqf/MsPacman_rew.png
new file mode 100644
index 000000000..6832017fb
Binary files /dev/null and b/examples/atari/results/fqf/MsPacman_rew.png differ
diff --git a/examples/atari/results/fqf/Pong_rew.png b/examples/atari/results/fqf/Pong_rew.png
new file mode 100644
index 000000000..e3a4e44fd
Binary files /dev/null and b/examples/atari/results/fqf/Pong_rew.png differ
diff --git a/examples/atari/results/fqf/Qbert_rew.png b/examples/atari/results/fqf/Qbert_rew.png
new file mode 100644
index 000000000..c0a2fec58
Binary files /dev/null and b/examples/atari/results/fqf/Qbert_rew.png differ
diff --git a/examples/atari/results/fqf/Seaquest_rew.png b/examples/atari/results/fqf/Seaquest_rew.png
new file mode 100644
index 000000000..2accab38e
Binary files /dev/null and b/examples/atari/results/fqf/Seaquest_rew.png differ
diff --git a/examples/atari/results/fqf/SpaceInvaders_rew.png b/examples/atari/results/fqf/SpaceInvaders_rew.png
new file mode 100644
index 000000000..fe271ecc1
Binary files /dev/null and b/examples/atari/results/fqf/SpaceInvaders_rew.png differ
diff --git a/test/discrete/test_fqf.py b/test/discrete/test_fqf.py
new file mode 100644
index 000000000..534927f12
--- /dev/null
+++ b/test/discrete/test_fqf.py
@@ -0,0 +1,153 @@
+import os
+import gym
+import torch
+import pprint
+import argparse
+import numpy as np
+from torch.utils.tensorboard import SummaryWriter
+
+from tianshou.policy import FQFPolicy
+from tianshou.utils import BasicLogger
+from tianshou.env import DummyVectorEnv
+from tianshou.utils.net.common import Net
+from tianshou.trainer import offpolicy_trainer
+from tianshou.utils.net.discrete import FractionProposalNetwork, FullQuantileFunction
+from tianshou.data import Collector, VectorReplayBuffer, PrioritizedVectorReplayBuffer
+
+
+def get_args():
+    parser = argparse.ArgumentParser()
+    parser.add_argument('--task', type=str, default='CartPole-v0')
+    parser.add_argument('--seed', type=int, default=0)
+    parser.add_argument('--eps-test', type=float, default=0.05)
+    parser.add_argument('--eps-train', type=float, default=0.1)
+    parser.add_argument('--buffer-size', type=int, default=20000)
+    parser.add_argument('--lr', type=float, default=3e-3)
+    parser.add_argument('--fraction-lr', type=float, default=2.5e-9)
+    parser.add_argument('--gamma', type=float, default=0.9)
+    parser.add_argument('--num-fractions', type=int, default=32)
+    parser.add_argument('--num-cosines', type=int, default=64)
+    parser.add_argument('--ent-coef', type=float, default=10.)
+    parser.add_argument('--n-step', type=int, default=3)
+    parser.add_argument('--target-update-freq', type=int, default=320)
+    parser.add_argument('--epoch', type=int, default=10)
+    parser.add_argument('--step-per-epoch', type=int, default=10000)
+    parser.add_argument('--step-per-collect', type=int, default=10)
+    parser.add_argument('--update-per-step', type=float, default=0.1)
+    parser.add_argument('--batch-size', type=int, default=64)
+    parser.add_argument('--hidden-sizes', type=int,
+                        nargs='*', default=[64, 64, 64])
+    parser.add_argument('--training-num', type=int, default=10)
+    parser.add_argument('--test-num', type=int, default=100)
+    parser.add_argument('--logdir', type=str, default='log')
+    parser.add_argument('--render', type=float, default=0.)
+    parser.add_argument('--prioritized-replay',
+                        action="store_true", default=False)
+    parser.add_argument('--alpha', type=float, default=0.6)
+    parser.add_argument('--beta', type=float, default=0.4)
+    parser.add_argument(
+        '--device', type=str,
+        default='cuda' if torch.cuda.is_available() else 'cpu')
+    args = parser.parse_known_args()[0]
+    return args
+
+
+def test_fqf(args=get_args()):
+    env = gym.make(args.task)
+    args.state_shape = env.observation_space.shape or env.observation_space.n
+    args.action_shape = env.action_space.shape or env.action_space.n
+    # train_envs = gym.make(args.task)
+    # you can also use tianshou.env.SubprocVectorEnv
+    train_envs = DummyVectorEnv(
+        [lambda: gym.make(args.task) for _ in range(args.training_num)])
+    # test_envs = gym.make(args.task)
+    test_envs = DummyVectorEnv(
+        [lambda: gym.make(args.task) for _ in range(args.test_num)])
+    # seed
+    np.random.seed(args.seed)
+    torch.manual_seed(args.seed)
+    train_envs.seed(args.seed)
+    test_envs.seed(args.seed)
+    # model
+    feature_net = Net(args.state_shape, args.hidden_sizes[-1],
+                      hidden_sizes=args.hidden_sizes[:-1], device=args.device,
+                      softmax=False)
+    net = FullQuantileFunction(
+        feature_net, args.action_shape, args.hidden_sizes,
+        num_cosines=args.num_cosines, device=args.device
+    )
+    optim = torch.optim.Adam(net.parameters(), lr=args.lr)
+    fraction_net = FractionProposalNetwork(args.num_fractions, net.input_dim)
+    fraction_optim = torch.optim.RMSprop(
+        fraction_net.parameters(), lr=args.fraction_lr
+    )
+    policy = FQFPolicy(
+        net, optim, fraction_net, fraction_optim, args.gamma, args.num_fractions,
+        args.ent_coef, args.n_step, target_update_freq=args.target_update_freq
+    ).to(args.device)
+    # buffer
+    if args.prioritized_replay:
+        buf = PrioritizedVectorReplayBuffer(
+            args.buffer_size, buffer_num=len(train_envs),
+            alpha=args.alpha, beta=args.beta)
+    else:
+        buf = VectorReplayBuffer(args.buffer_size, buffer_num=len(train_envs))
+    # collector
+    train_collector = Collector(policy, train_envs, buf, exploration_noise=True)
+    test_collector = Collector(policy, test_envs, exploration_noise=True)
+    # policy.set_eps(1)
+    train_collector.collect(n_step=args.batch_size * args.training_num)
+    # log
+    log_path = os.path.join(args.logdir, args.task, 'fqf')
+    writer = SummaryWriter(log_path)
+    logger = BasicLogger(writer)
+
+    def save_fn(policy):
+        torch.save(policy.state_dict(), os.path.join(log_path, 'policy.pth'))
+
+    def stop_fn(mean_rewards):
+        return mean_rewards >= env.spec.reward_threshold
+
+    def train_fn(epoch, env_step):
+        # eps annnealing, just a demo
+        if env_step <= 10000:
+            policy.set_eps(args.eps_train)
+        elif env_step <= 50000:
+            eps = args.eps_train - (env_step - 10000) / \
+                40000 * (0.9 * args.eps_train)
+            policy.set_eps(eps)
+        else:
+            policy.set_eps(0.1 * args.eps_train)
+
+    def test_fn(epoch, env_step):
+        policy.set_eps(args.eps_test)
+
+    # trainer
+    result = offpolicy_trainer(
+        policy, train_collector, test_collector, args.epoch,
+        args.step_per_epoch, args.step_per_collect, args.test_num,
+        args.batch_size, train_fn=train_fn, test_fn=test_fn,
+        stop_fn=stop_fn, save_fn=save_fn, logger=logger,
+        update_per_step=args.update_per_step)
+    assert stop_fn(result['best_reward'])
+
+    if __name__ == '__main__':
+        pprint.pprint(result)
+        # Let's watch its performance!
+        env = gym.make(args.task)
+        policy.eval()
+        policy.set_eps(args.eps_test)
+        collector = Collector(policy, env)
+        result = collector.collect(n_episode=1, render=args.render)
+        rews, lens = result["rews"], result["lens"]
+        print(f"Final reward: {rews.mean()}, length: {lens.mean()}")
+
+
+def test_pfqf(args=get_args()):
+    args.prioritized_replay = True
+    args.gamma = .95
+    test_fqf(args)
+
+
+if __name__ == '__main__':
+    test_fqf(get_args())
diff --git a/tianshou/policy/__init__.py b/tianshou/policy/__init__.py
index a35089131..9dd879cb1 100644
--- a/tianshou/policy/__init__.py
+++ b/tianshou/policy/__init__.py
@@ -4,6 +4,7 @@
 from tianshou.policy.modelfree.c51 import C51Policy
 from tianshou.policy.modelfree.qrdqn import QRDQNPolicy
 from tianshou.policy.modelfree.iqn import IQNPolicy
+from tianshou.policy.modelfree.fqf import FQFPolicy
 from tianshou.policy.modelfree.pg import PGPolicy
 from tianshou.policy.modelfree.a2c import A2CPolicy
 from tianshou.policy.modelfree.npg import NPGPolicy
@@ -28,6 +29,7 @@
     "C51Policy",
     "QRDQNPolicy",
     "IQNPolicy",
+    "FQFPolicy",
     "PGPolicy",
     "A2CPolicy",
     "NPGPolicy",
diff --git a/tianshou/policy/modelfree/fqf.py b/tianshou/policy/modelfree/fqf.py
new file mode 100644
index 000000000..db110cc79
--- /dev/null
+++ b/tianshou/policy/modelfree/fqf.py
@@ -0,0 +1,161 @@
+import torch
+import numpy as np
+import torch.nn.functional as F
+from typing import Any, Dict, Optional, Union
+
+from tianshou.policy import DQNPolicy, QRDQNPolicy
+from tianshou.data import Batch, to_numpy, ReplayBuffer
+from tianshou.utils.net.discrete import FractionProposalNetwork, FullQuantileFunction
+
+
+class FQFPolicy(QRDQNPolicy):
+    """Implementation of Fully-parameterized Quantile Function. arXiv:1911.02140.
+
+    :param torch.nn.Module model: a model following the rules in
+        :class:`~tianshou.policy.BasePolicy`. (s -> logits)
+    :param torch.optim.Optimizer optim: a torch.optim for optimizing the model.
+    :param FractionProposalNetwork fraction_model: a FractionProposalNetwork for
+        proposing fractions/quantiles given state.
+    :param torch.optim.Optimizer fraction_optim: a torch.optim for optimizing
+        the fraction model above.
+    :param float discount_factor: in [0, 1].
+    :param int num_fractions: the number of fractions to use. Default to 32.
+    :param float ent_coef: the coefficient for entropy loss. Default to 0.
+    :param int estimation_step: the number of steps to look ahead. Default to 1.
+    :param int target_update_freq: the target network update frequency (0 if
+        you do not use the target network).
+    :param bool reward_normalization: normalize the reward to Normal(0, 1).
+        Default to False.
+
+    .. seealso::
+
+        Please refer to :class:`~tianshou.policy.QRDQNPolicy` for more detailed
+        explanation.
+    """
+
+    def __init__(
+        self,
+        model: FullQuantileFunction,
+        optim: torch.optim.Optimizer,
+        fraction_model: FractionProposalNetwork,
+        fraction_optim: torch.optim.Optimizer,
+        discount_factor: float = 0.99,
+        num_fractions: int = 32,
+        ent_coef: float = 0.0,
+        estimation_step: int = 1,
+        target_update_freq: int = 0,
+        reward_normalization: bool = False,
+        **kwargs: Any,
+    ) -> None:
+        super().__init__(
+            model, optim, discount_factor, num_fractions, estimation_step,
+            target_update_freq, reward_normalization, **kwargs
+        )
+        self.propose_model = fraction_model
+        self._ent_coef = ent_coef
+        self._fraction_optim = fraction_optim
+
+    def _target_q(self, buffer: ReplayBuffer, indice: np.ndarray) -> torch.Tensor:
+        batch = buffer[indice]  # batch.obs_next: s_{t+n}
+        if self._target:
+            result = self(batch, input="obs_next")
+            a, fractions = result.act, result.fractions
+            next_dist = self(
+                batch, model="model_old", input="obs_next", fractions=fractions
+            ).logits
+        else:
+            next_b = self(batch, input="obs_next")
+            a = next_b.act
+            next_dist = next_b.logits
+        next_dist = next_dist[np.arange(len(a)), a, :]
+        return next_dist  # shape: [bsz, num_quantiles]
+
+    def forward(
+        self,
+        batch: Batch,
+        state: Optional[Union[dict, Batch, np.ndarray]] = None,
+        model: str = "model",
+        input: str = "obs",
+        fractions: Optional[Batch] = None,
+        **kwargs: Any,
+    ) -> Batch:
+        model = getattr(self, model)
+        obs = batch[input]
+        obs_ = obs.obs if hasattr(obs, "obs") else obs
+        if fractions is None:
+            (logits, fractions, quantiles_tau), h = model(
+                obs_, propose_model=self.propose_model, state=state, info=batch.info
+            )
+        else:
+            (logits, _, quantiles_tau), h = model(
+                obs_, propose_model=self.propose_model, fractions=fractions,
+                state=state, info=batch.info
+            )
+        weighted_logits = (
+            fractions.taus[:, 1:] - fractions.taus[:, :-1]
+        ).unsqueeze(1) * logits
+        q = DQNPolicy.compute_q_value(
+            self, weighted_logits.sum(2), getattr(obs, "mask", None)
+        )
+        if not hasattr(self, "max_action_num"):
+            self.max_action_num = q.shape[1]
+        act = to_numpy(q.max(dim=1)[1])
+        return Batch(
+            logits=logits, act=act, state=h, fractions=fractions,
+            quantiles_tau=quantiles_tau
+        )
+
+    def learn(self, batch: Batch, **kwargs: Any) -> Dict[str, float]:
+        if self._target and self._iter % self._freq == 0:
+            self.sync_weight()
+        weight = batch.pop("weight", 1.0)
+        out = self(batch)
+        curr_dist_orig = out.logits
+        taus, tau_hats = out.fractions.taus, out.fractions.tau_hats
+        act = batch.act
+        curr_dist = curr_dist_orig[np.arange(len(act)), act, :].unsqueeze(2)
+        target_dist = batch.returns.unsqueeze(1)
+        # calculate each element's difference between curr_dist and target_dist
+        u = F.smooth_l1_loss(target_dist, curr_dist, reduction="none")
+        huber_loss = (u * (
+            tau_hats.unsqueeze(2) - (target_dist - curr_dist).detach().le(0.).float()
+        ).abs()).sum(-1).mean(1)
+        quantile_loss = (huber_loss * weight).mean()
+        # ref: https://github.com/ku2482/fqf-iqn-qrdqn.pytorch/
+        # blob/master/fqf_iqn_qrdqn/agent/qrdqn_agent.py L130
+        batch.weight = u.detach().abs().sum(-1).mean(1)  # prio-buffer
+        # calculate fraction loss
+        with torch.no_grad():
+            sa_quantile_hats = curr_dist_orig[np.arange(len(act)), act, :]
+            sa_quantiles = out.quantiles_tau[np.arange(len(act)), act, :]
+            # ref: https://github.com/ku2482/fqf-iqn-qrdqn.pytorch/
+            # blob/master/fqf_iqn_qrdqn/agent/fqf_agent.py L169
+            values_1 = sa_quantiles - sa_quantile_hats[:, :-1]
+            signs_1 = sa_quantiles > torch.cat([
+                sa_quantile_hats[:, :1], sa_quantiles[:, :-1]], dim=1)
+
+            values_2 = sa_quantiles - sa_quantile_hats[:, 1:]
+            signs_2 = sa_quantiles < torch.cat([
+                sa_quantiles[:, 1:], sa_quantile_hats[:, -1:]], dim=1)
+
+            gradient_of_taus = (
+                torch.where(signs_1, values_1, -values_1)
+                + torch.where(signs_2, values_2, -values_2)
+            )
+        fraction_loss = (gradient_of_taus * taus[:, 1:-1]).sum(1).mean()
+        # calculate entropy loss
+        entropy_loss = out.fractions.entropies.mean()
+        fraction_entropy_loss = fraction_loss - self._ent_coef * entropy_loss
+        self._fraction_optim.zero_grad()
+        fraction_entropy_loss.backward(retain_graph=True)
+        self._fraction_optim.step()
+        self.optim.zero_grad()
+        quantile_loss.backward()
+        self.optim.step()
+        self._iter += 1
+        return {
+            "loss": quantile_loss.item() + fraction_entropy_loss.item(),
+            "loss/quantile": quantile_loss.item(),
+            "loss/fraction": fraction_loss.item(),
+            "loss/entropy": entropy_loss.item()
+        }
diff --git a/tianshou/utils/net/discrete.py b/tianshou/utils/net/discrete.py
index 14cc85e50..b104b4ee8 100644
--- a/tianshou/utils/net/discrete.py
+++ b/tianshou/utils/net/discrete.py
@@ -4,6 +4,7 @@
 import torch.nn.functional as F
 from typing import Any, Dict, Tuple, Union, Optional, Sequence
 
+from tianshou.data import Batch
 from tianshou.utils.net.common import MLP
 
 
@@ -199,6 +200,110 @@ def forward(  # type: ignore
         embedding = (logits.unsqueeze(1) * self.embed_model(taus)).view(
             batch_size * sample_size, -1
         )
-        out = self.last(embedding).view(batch_size,
-                                        sample_size, -1).transpose(1, 2)
+        out = self.last(embedding).view(
+            batch_size, sample_size, -1).transpose(1, 2)
         return (out, taus), h
+
+
+class FractionProposalNetwork(nn.Module):
+    """Fraction proposal network for FQF.
+
+    :param num_fractions: the number of factions to propose.
+    :param embedding_dim: the dimension of the embedding/input.
+
+    .. note::
+
+        Adapted from https://github.com/ku2482/fqf-iqn-qrdqn.pytorch/blob/master
+        /fqf_iqn_qrdqn/network.py .
+    """
+
+    def __init__(self, num_fractions: int, embedding_dim: int) -> None:
+        super().__init__()
+        self.net = nn.Linear(embedding_dim, num_fractions)
+        torch.nn.init.xavier_uniform_(self.net.weight, gain=0.01)
+        torch.nn.init.constant_(self.net.bias, 0)
+        self.num_fractions = num_fractions
+        self.embedding_dim = embedding_dim
+
+    def forward(
+        self, state_embeddings: torch.Tensor
+    ) -> Tuple[torch.Tensor, torch.Tensor, torch.Tensor]:
+        # Calculate (log of) probabilities q_i in the paper.
+        m = torch.distributions.Categorical(logits=self.net(state_embeddings))
+        taus_1_N = torch.cumsum(m.probs, dim=1)
+        # Calculate \tau_i (i=0,...,N).
+        taus = F.pad(taus_1_N, (1, 0))
+        # Calculate \hat \tau_i (i=0,...,N-1).
+        tau_hats = (taus[:, :-1] + taus[:, 1:]).detach() / 2.0
+        # Calculate entropies of value distributions.
+        entropies = m.entropy()
+        return taus, tau_hats, entropies
+
+
+class FullQuantileFunction(ImplicitQuantileNetwork):
+    """Full(y parameterized) Quantile Function.
+
+    :param preprocess_net: a self-defined preprocess_net which output a
+        flattened hidden state.
+    :param int action_dim: the dimension of action space.
+    :param hidden_sizes: a sequence of int for constructing the MLP after
+        preprocess_net. Default to empty sequence (where the MLP now contains
+        only a single linear layer).
+    :param int num_cosines: the number of cosines to use for cosine embedding.
+        Default to 64.
+    :param int preprocess_net_output_dim: the output dimension of
+        preprocess_net.
+
+    .. note::
+
+        The first return value is a tuple of (quantiles, fractions, quantiles_tau),
+        where fractions is a Batch(taus, tau_hats, entropies).
+    """
+
+    def __init__(
+        self,
+        preprocess_net: nn.Module,
+        action_shape: Sequence[int],
+        hidden_sizes: Sequence[int] = (),
+        num_cosines: int = 64,
+        preprocess_net_output_dim: Optional[int] = None,
+        device: Union[str, int, torch.device] = "cpu",
+    ) -> None:
+        super().__init__(
+            preprocess_net, action_shape, hidden_sizes,
+            num_cosines, preprocess_net_output_dim, device
+        )
+
+    def _compute_quantiles(
+        self, obs: torch.Tensor, taus: torch.Tensor
+    ) -> torch.Tensor:
+        batch_size, sample_size = taus.shape
+        embedding = (obs.unsqueeze(1) * self.embed_model(taus)).view(
+            batch_size * sample_size, -1
+        )
+        quantiles = self.last(embedding).view(
+            batch_size, sample_size, -1
+        ).transpose(1, 2)
+        return quantiles
+
+    def forward(  # type: ignore
+        self, s: Union[np.ndarray, torch.Tensor],
+        propose_model: FractionProposalNetwork,
+        fractions: Optional[Batch] = None,
+        **kwargs: Any
+    ) -> Tuple[Any, torch.Tensor]:
+        r"""Mapping: s -> Q(s, \*)."""
+        logits, h = self.preprocess(s, state=kwargs.get("state", None))
+        # Propose fractions
+        if fractions is None:
+            taus, tau_hats, entropies = propose_model(logits.detach())
+            fractions = Batch(taus=taus, tau_hats=tau_hats, entropies=entropies)
+        else:
+            taus, tau_hats = fractions.taus, fractions.tau_hats
+        quantiles = self._compute_quantiles(logits, tau_hats)
+        # Calculate quantiles_tau for computing fraction grad
+        quantiles_tau = None
+        if self.training:
+            with torch.no_grad():
+                quantiles_tau = self._compute_quantiles(logits, taus[:, 1:-1])
+        return (quantiles, fractions, quantiles_tau), h