In this paper, we present a time-dependent quantum wave packet calculation based on the Alexander-Stark-Werner (ASW) potential energy surfaces (PESs) to study the reactivity of the ground and excited spin-orbit states for the reaction of F(P-2(3/2),P-2(1/2)) with D-2 (nu = j = 0). The reaction probabilities and the integral cross sections are calculated. Furthermore, the multistate cross sections are compared with the single-state calculation. The multistate cross section is smaller than the single-state calculation at higher collision energy. The effect of the nonadiabatic coupling becomes more and more obvious as the collision energy increases. The overall reactivity of the excited state of F is, at most, 25% of that of the ground spin-orbit states. The threshold energy of the F(P-2(3/2)) + D-2 reaction is similar to0.10 kcal/mol. The contributions of the excited state of F are 0.9% and 3.1% of the total average rate constant, at 200 and 500 K, respectively. The effect of the excited spin-orbit state rate constant to the average rate constant is very small but grows slowly as the temperature increases.