Abstract: The time-dependent wave packet propagation method was applied to investigate the dynamic behaviours of the reaction S^-(^2P)+H_2(^1\Sigma_\rmg^+)\rightarrow SH^-(^1\Sigma)+H(^2S) based on the electronic ground state (^2A') potential energy surface of the SH_2^- ionic molecule. The collision energy dependent reaction probabilities and integral cross sections are obtained. The numerical results suggest that there are significant oscillation structures over all the studied range of the collision energies. The vibrational excitation and rotational excitation of the diatomic reagent H_2 promote the reactivity significantly as suggested by the numerical total reaction probabilities with the initial rotational quantum number of j=0, 2, 4, 6, 8, 10, and the vibrational quantum number v=0, 1, 2, 3, 4. The numerical integral cross sections are quite consistent with the experimental data reported in previous work.