Quasi-classical trajectory (QCT) calculations of H+HBr $\rightarrow$ H2 + Br reaction have been performed on a recently proposed ab initio potential energy surface. The reaction probability and integral cross section are found to be in fairly good agreement with the available quantum mechanical (QM) results on this surface. The behavior of reactivity is well consistent with properties of exothermic reaction. Once the energy of vibrational excited HBr is larger than the barrier height, the integral cross sections for the reaction diverge at very low collision energies close to the threshold, similarly to capture reaction. In addition, differential cross sections show that scattering of the product H2 shift from backward to forward directions as the collision energy and vibrational quantum number increase. All the theoretical findings are reasonably explained by the properties of the surface, as well as reactive mechanisms.