Recently the GaN/AlN multi-quantum-well structure avalanche photodiode (MAPD) has been demonstrated with PMT-like multiplication gain larger than 1E4. In this work, the photocurrent of GaN/AlN MAPD has been investigated and negative differential conductance (NDC) is found in the photocurrent characteristic of MAPD. Through self-consistent calculation, conduction band structure and discrete energy states in each quantum well layer have been obtained for MAPD. The discrete states drop down and align with the conduction band edge of absorption layer around the NDC peak voltage, so the NDC feature is proposed as resonant tunneling of photoelectrons into MQW structure. The proposed resonant tunneling process is confirmed by the observation of resonant tunneling peaks in a specially designed resonant tunneling diode simulating the band profile of MAPD. The finding of NDC feature is beneficial for understanding and increasing the quantum efficiency of MAPD, since the photoelectron blocking at AlN barrier is greatly reduced by the resonant tunneling process.