The reaction of gas-phase hydrogen atoms H with H atoms chemisorbed on a graphite surface has been studied by the classical dynamics. The graphite surface is composed of the surface and 10 inner layers at various gas and surface temperatures (Tg, Ts). Three chains in the surface layer and 13 chains through the inner layers are considered to surround the adatom site. Four reaction pathways are found: H2 formation, H-H exchange, H desorption, and H adsorption. At (1500 K, 300 K), the probabilities of H2 formation and H desorption are 0.28 and 0.24, respectively, whereas those of the other two pathways are in the order of 10-2. Half the reaction energy deposits in the vibrational motion of H2, thus leading to a highly excited state. The majority of the H2 formation results from the chemisorption-type H(g)-surface interaction. Vibrational excitation is found to be strong for H2 formed on a cold surface (~10 K), exhibiting a pronounced vibrational population inversion. Over the temperature range (10-100 K, 10 K), the probabilities of H2 formation and H-H exchange vary from 0 to ~0.1, but the other two probabilities are in the order of 10-3.