The structures and electronic states of sodium atom (Na) trapped on the graphene surfaces have been investigated by means of density functional theory (DFT) calculation to elucidate the nature of interaction between Na and the graphenes. In addition, direct molecular orbital-molecular dynamics (MO-MD) calculation [Tachikawa, J. Phys. Chem. C, 112 (2008) 10193] was applied to diffusion processes of the Na atom on graphene surfaces. Seven graphenes (n = 7, 14, 19, 29, 37, 44 and 52, where n means numbers of rings in each carbon cluster) were examined in the present study. The B3LYP/LANL2MB calculation showed that the sodium atom is located at ca. 3.0 angstrom from the graphene surfaces. The direct MO-MD calculation showed that diffusion of Na atom is slower than that of Na(+) ion on graphene surface. The nature of the interaction between Na atom and the carbon clusters was discussed on the basis of theoretical results.