The adsorption of Li atom on graphene is examined using density functional theory methods. Three different adsorption sites are considered, including the on top of a carbon atom (OT), on top of a C C bond (Bri), and on top of a hexagon (Hol), as well as Li adsorbed at different coverage. The Hol site is found to be the most stable, followed by the Bri and OT sites. The order of stabilization is independent of coverage. The localization of Li-graphene interaction at all sites has reverse order with stabilization. The localization will cause different repulsive interaction between Li atoms which is believed to take responsibility for the difference between the charge transfer order and adsorption energy order of Li adsorption at all possible sites. Repulsive interaction also causes the decreasing of adsorption energies of Li at Hol site with increasing coverage, but the corresponding influence is bigger at low coverage range (0.020-0.056 monolayers) than that at high coverage range (0.056-0.250 monolayers). The trend of charge transfer and dipole moment with increasing coverage is also in agreement with that of adsorption energy. It is also found that the distance of Li above graphene will increase with increasing coverage, but a so-called "zigzag" curve appears, which exhibits an oscillatory behavior as a function of increasing coverage. The diffusion of Li atom on graphene is also studied. Li atom migrates from a Hol site to a neighboring Hol site through the Bri site between them is found to be the minimum energy path. Within the studied coverage range, the diffusion barrier decreases with increasing coverage which can be ascribed to the phenomenon of different repulsion interactions when Li atom adsorbs at different sites. The increasing coverage amplified the phenomenon. (C) 2013 Elsevier B.V. All rights reserved.