We have carried out first-principles calculations on electronic properties of
graphene quantum dots embedded in hexagonal boron nitride monolayer sheets. The
calculations with density functional theory show that the band gaps of quantum
dots are determined by the quantum confinement effects and the hybridization of
{\pi} orbitals from B, N and C atoms. The energy states near the Fermi level
are found to be strongly localized within and in the vicinity of the quantum
dots