The lowest triplet state of the H2O2 system features multiple reaction channels, including several relevant to the combustion of H2. To accurately map out the global potential energy surface, ~28 000 geometries were sampled over a large configuration space including all important asymptotes, and electronic energies at these points were calculated at the level of the explicitly correlated version of the multi-reference configuration interaction (MRCI-F12) method. A new multi-channel global potential energy surface was constructed by fitting the ab initio data set using a permutation invariant polynomial-neural network method, resulting in a total root mean square fitting error of only 6.7 meV (0.15 kcal mol-1). Various kinetics and dynamical properties of several relevant reactions were calculated on the new MRCI potential energy surface, and compared with the available experimental results.