An accurate global potential energy surface (PES) for the HBr2 system has been constructed using the fundamental invariant neural network fitting method based upon 11 698 ab initio energies at the UCCSD(T)/CBS level of theory, with the spin-orbit coupling of the 2P3/2 orbit of the Br atom properly included. The time-dependent wave packet calculations have been performed to study the H + Br2 → HBr + Br reaction on the new PES. The total reaction probabilities for total angular momentum J = 0 for the ground initial state show no threshold due to the submerged barrier height (-0.351 kcal/mol) of the PES. The total integral cross sections (ICS) for reactant Br2 in ro-vibrational states (v0 = 0, j0 = 0, 10, 20, 30; v0 = 1-5, j0 = 0) were calculated for collision energy of up to 0.5 eV. It is found that the initial rotational excitation has a negligible effect on the ICS, and the initial vibrational excitation depresses the reactivity to some extent. The thermal rate constants for the title reaction in the temperature range of 100-1000 K were calculated from the Boltzmann averaging of the v0 = 0-5 rate constants, which overestimated the experimental results to some extent.