The reaction of gas-phase atomic hydrogen with hydrogen atoms chemisorbed on a silicon surface is studied by use of the classical trajectory approach. Especially, we have focused on the mechanism changes with the hydrogen surface coverage difference. On the sparsely covered surface, the gas atom interacts with the preadsorbed hydrogen atom and adjacent bare surface sites. In this case, it is shown that the chemisorption of H(g) is of major importance. Nearly all of the chemisorption events accompany the desorption of H(ad), i.e., adisplacement reaction. Although much less important than the displacement reaction, the formation of $H_2(g)$ is the second most significant reaction pathway. At gas temperature of 1800 K and surface temperature of 300 K, the probabilities of these two reactions are 0.750 and 0.065, respectively. The adsorption of H(g) without dissociating H(ad) is found to be negligible. In the reaction pathway forming $H_2$, most of the reaction energy is carried by $H_2(g)$. Although the majority of $H_2(g)$ molecules are produced in sub-picosecond, direct-mode collisions, there is a small amount of $H_2(g)$ produced in multiple impact collisions, which is characteristic of complex-mode collisions. On the fully covered surface, it has been shown that the formation of $H_2(g)$ is of major importance. All reactive events occur on a subpicosecond scale, following the Eley-Rideal mechanism. At gas temperature of 1800 K and surface temperature of 300 K, the probability of the $H_2(g)$ formation reaction is 0.082. In this case, neither the gas atom trapping nor the displacement reaction has been found.