The stabilities and atomic geometries of the graphene adatom and its dimer are studied using first-principles calculations based on the density functional theory. In the most stable structure, the adatom is located above the bond-center site. We also found a metastable structure whose formation energy is slightly (0.25 eV) higher than the most stable structure. The diffusion barrier of the adatom is estimated to be 0.44 eV. Then, dimers are expected to be formed by the diffusion of the adatom. The dimer has three stable structures whose formation energies are close to each other. Since the dissociation energies of these structures are large (5.90-5.93 eV), the dimers are energetically stable. Therefore these structures are expected to be detected under some experimental conditions. [DOI: 10.1380/ejssnt.2008.269]