Theoretical studies of the dynamics of the abstraction reaction, H' + HBr (v=0, j=0) -> H'H + Br, have been performed with quasiclassical trajectory method (QCT) on a new ab initio potential energy surface (Y. Kurosaki and T. Takayanagi, private communication). The calculated QCT cross sections are in good agreement with earlier quantum wave packet results over most of the collision energy range from 0.1 to 2.6 eV, and the state-resolved rotational distributions of the product H'H molecule are quantitatively consistent with the experimental results. Comparisons of the QCT-calculated rotational-state-resolved cross sections on different potential energy surfaces show that the characteristics of the potential energy surface in the region far away from the minimum energy path have a large influence on the title abstraction reaction dynamics, and the indirect reactions that do not follow the minimum energy path have little influence on the differential cross sections (DCS). The DCSs are mainly governed by the direct reactions that do follow the minimum energy path, at both low and high collision energies. The degree of the rotational alignment of the product H'H molecule is strong at high collision energies, which means that the influence of the indirect reactions on the product rotational alignment is negligible, whereas the distribution of P(phi(r)) is sensitive to the indirect reactions at high collision energies. With increasing collision energy, the polarization of the product rotational angular momentum decreases and the molecular rotation of the product prefers an in-plane reaction mechanism rather than the out-of-plane mechanism.