Initial state-selected and energy resolved reaction probabilities, integral cross sections（ICS） and the thermal rate constants of the H( ²S)+ SiH (X ²П; v=0, j=0)→Si( ¹D)+H ₂(X ¹Σ< _i>g ⁺) reaction are calculated within coupled states（CS） approximation and accurate calculation with full Coriolis coupling（CC） by a time-dependent wave packet propagation method (Chebyshev wave packet method). The new ab initio global potential energy surface (PES) of the electronic ground state (1 ¹A') of the system, recently reported by Li et al. [ Phys. Chem. Chem. Phys., 2022, 24, 7759], is employed for the purpose. All partial wave contributions up to the total angular momentum J=80 for CS approximation and J=90 for CC calculation are considered to obtain the converged ICSs over a collision energy range of 1.0×10 ^-3-1.0 eV. The calculated probabilities and ICSs display a decreasing trend with the increase of the collision energy and show an oscillatory structure due to the SiH ₂well on the reaction path. The neglect of CC effect will lead to underestimation of the ICS and the rate constant due to the formation of a SiH ₂complex supported by the stationary points of the SiH ₂（1 ¹A'）PES. In addition, the results of the exact calculation including CC effect are compared with those from the CS approximation. For the reaction probability, a similar trend of CC and CS calculations are observed at small total angular momentum J=10, 20 and 30, and the CC results are larger than the latter almost in the whole considered energy range at large total angular momentum J=40, 50, 60 and 70. The gap between CS and CC probabilities are increasing as Jincreases which reveals that Coriolis coupling effects get more and more important with increasing of Jfor the title reaction. Moreover, the exact quantum wave calculations show that the thermal rate constants between 300 K and 1000 K for the title reaction shows a temperature independent behavior similar to the H + CH reaction, but the value of the rate constant for the H + SiH reaction is an order of magnitude larger than that of the H + CH reaction.