In this paper, we employ the time-dependent quantum wave packet method to study the reaction of F(P-2(3/2), P-2(1/2)) with HD on the Alexander-Stark-Werner potential energy surface. The reaction probabilities and total integral cross sections of the spin-orbit ground and excited states for the two possible products of the system are calculated. Because the reaction channel of the excited spin-orbit state is closed at the resonance energy, the resonance feature does not appear in the reaction probabilities and cross section for the F(P-2(1/2))+HD(v=j=0)-->HF+D reaction, in contrast with that found for the ground spin-orbit state. We also compare the average cross sections of the two possible products with the experimental measurement. The resonance peak in the present average cross section for the HF+D product is slightly larger than the experimental result, but much smaller than that of the single-state calculations on the potential energy surface of Stark and Werner. It seems that the spin-orbit coupling would play a relatively important role in this reaction. Moreover, the isotope effects of the ground and excited spin-orbit states and the reactivity of the two product channels from the excited spin-orbit state are presented. (C) 2004 American Institute of Physics.