The interaction between graphene and a SiO(2) surface has been analyzed with first-principles DFT calculations by constructing the different configurations based on α-quartz and cristobalite structures. The fact that single-layer graphene can stay stably on a SiO(2) surface is explained based on a general consideration of the configuration structures of the SiO(2) surface. It is found that the oxygen defect in a SiO(2) surface can shift the Fermi level of graphene down which opens up the mechanism of the hole-doping effect of graphene adsorbed on a SiO(2) surface observed in a lot of experiments.