Charge transport properties of a diffusive normal metal∕triplet superconductor (DN∕TS) junction are studied based on the Keldysh-Nambu quasiclassical Green’s function formalism. Contrary to the unconventional singlet superconductor junction case, the mid-gap Andreev resonant state at the interface of the TS is shown to enhance the proximity effect in the DN. The total resistance of the DN∕TS junction is drastically reduced and is completely independent of the resistance of the DN in the extreme case. Such anomalous transport accompanies a giant zero-bias peak in the conductance spectra and a zero-energy peak of the local density of states in the DN region. These striking features manifest the presence of novel proximity effect peculiar to triplet superconductor junctions.