In this work, the graphene/α-SiO2(0001) interface is calculated using density functional theory. On the oxygen-terminated SiO2 surface, atomic structure reconstruction occurs at the graphene/SiO2 interface to eliminate the dangling bonds. The interface interaction is 77 meV/C atom, which indicates that van der Waals force dominates the interaction, but it is stronger than the force between the graphene layers in graphite. The distance between graphene and the SiO2 surface is 2.805 Å, which is smaller than the 3.4 Å interlayer distance of graphite. In addition, the SiO2 substrate induces p-type doping in graphene and opens a small gap of 0.13 eV at the Dirac point of graphene, which is desirable for electronic device applications.