The initial state-resolved reaction probabilities, reaction cross-sections, and rate constants of the reaction Br + HD are computed on 3 potential energy surfaces (denoted as e-LEPS, MB2, and MB3, respectively) by carrying out quantum time-dependent wave packet calculations. The results show that the reactivity of Br + HD on MB3 is much stronger than that on e-LEPS and somewhat weaker than that on MB2. Both of the vibrational and the rotational excitation of reagent HD enhance the reaction, which depends on the PESs and the strongest enhancement effects are on e-LEPS.