A system with periodical structure of graphite, in which a Li or H atom is set in the center of the supercell, has been simulated by molecular dynamics method to study the thermal diffusion of Li and H in the bulk graphite. It is found that the rates of diffusion of both Li and H atoms increase with the increase of the simulation temperature: from 50 K to 200 K, and the specific diffusive rates and behaviors for Li and H are different according to their trajectories. The diffusive curves for Li can be classified into three types, while H has only one type of diffusive curve, which shows that the interaction between Li and carbon is weaker than that between H and carbon. The conductive band gap of graphite is also calculated by the extended Huckel method. The gap is broadened by about 0.1 eV when graphite is intercalated with H, but the gap remains unchanged when graphite is intercalated with Li. It indicates that the addition of Li does not influence the conduction characteristic of graphite while that of H does. Thus Li-GIC (Graphite Intercalated Compound) is proposed to be a favorable material for the electrode.