The quantum dynamics of the Cl+D-2 reaction has been studied by means of time-dependent quantum wave packet calculations on the G3 and BW2 potential energy surfaces. Initial state-specific total reaction probabilities and integral cross sections are calculated, and the thermal rate constant is obtained. On the G3 surface, the effect of the reagent's rotational excitation on the reactivity is negative, while on the BW2 surface, the rotation of reagent has positive effect on the reactivity. Comparison of the thermal rate constants on the G3 and BW2 surfaces with experimental measurement is shown.