Time-dependent quantum wave packet calculations were carried out for the F + HBr reaction on the latest London-Erying-Polanyi-Sato potential energy surface constructed by Persky et al. The calculated reaction probabilities dramatically increase near the zero collision energy and then slightly decrease with increasing collision energy, which corresponds well to the behavior of a barrierless reaction. The effects of reagent HBr excitation were examined, it is shown that both the vibrational and the rotational excitations of reagent HBr have a negative effect on the reactivity of F + HBr. The integral cross-section for the ground state of the reagent HBr decreases at a low collision energy and then becomes plat with increasing collision energy, which is reasonable for the feasibility of such an exothermal reaction. The rate constant that was obtained is slightly higher than that obtained in the quasi-classical trajectory calculation.