The dynamics of the N-2 + HOC+ multichannel reaction is investigated up to 1.0 eV of collision energy on an accurate global potential energy surface (PES) for the ground electronic state. The PES is constructed using the permutation invariant polynomial-neural network (PIP-NN) method by fitting similar to 37 000 points at the CCSD-(T)-F12a/cc-pVTZ-F12 level with a root-mean-square error of about 3.0 meV. It was found that the total reaction integral cross section decreases monotonically with the collision energy, consistent with the barrierless complex-forming mechanism. Throughout the energy range, the proton transfer channel, which leads to the N2H+ + CO products, dominates the proton isomerization channel, which forms the N-2 + HCO+ products. The differential cross section of the proton transfer channel is backward biased, signaling a relatively direct process, while that of the proton isomerization channel shows strong forward-backward symmetry, which can be attributed to a long-lived intermediate.