The structures and electronic states of sodium ion (Na(+)) trapped on the graphene 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) 101931 was applied to diffusion processes of the Na(+) ion on graphene. The graphene composed of 37 benzene rings was used as a model of graphene. The B3LYP/LANL2MB calculation showed that the sodium ion is stabilized in hexagonal site and is located at ca. 2.230 angstrom from the graphene surfaces. The direct MO-MD calculation showed that the Na(+) ion diffuses freely on the graphene surface, but the ion did not approach the edge region due to the fact that a high potential barrier exists near the edge region. The nature of interaction between Na(+) and graphene was discussed on the basis of theoretical results. (C) 2009 Elsevier B.V. All rights reserved.