The thermal rate coefficients of H + H2O2 -> OH + H2O were obtained theoretically based on a recent fundamental invariant-neural network potential energy surface. The ring polymer molecular dynamics (RPMD) calculations were performed to get the rate coefficients with quantum effects, which are in good accord with some experimental values. The rate coefficients derived from extensive quasi-classical trajectory and canonical variational transition-state calculations also predict well the experimental results at high temperatures. The RPMD rate coefficients for H + H2O2 -> OH + H2O are larger than H + H2O2 -> H-2 + H2O, but at very low temperatures below the room temperature, the H-2 + HO2 channel becomes dominant due to significant quantum tunneling effects in the H atom transfer process. Considering that the old experimental values vary widely from different groups, we expect that our theoretical investigations can motivate new experimental work, which facilitates a more reliable comparison between theory and experiment.