The interaction of carbon free radicals (CH and CCH) with a graphene surface has been investigated by means of density functional theory (DFT) method in order to elucidate the radical scavenge mechanism of graphene surface. These radicals are highly reactive and the radical plays an important part of materials chemistry. The DFT calculation showed that the CH and CCH radicals bind to the bond center of C-C carbon atoms as a carbon bridge and a strong C-CH-C bond (or C-C2H-C bond) is formed. The binding energies of CH and CCH radicals to the graphene were calculated to be 48.2 and 46.2 kcal/mol at the B3LYP/6-31G(d) level of theory. The mechanism of CH radical addition was discussed on the basis of theoretical results.