We introduce graphene into conventional photonic crystals to build new photonic crystal structures, and strictly derive the dispersion relations of the structures based on the electromagnetic boundary conditions and the Maxwell's equations required. The dispersion relations are different from that of the conventional photonic crystals, and the optical properties of the structures may also differ from that of the conventional photonic crystals because of the presence of graphene conductivity in the dispersion relations. By changing the Fermi energy of graphene, the conductivity of it can be changed, the dispersion relations adjusted, the energy band structure altered, and its light propagation manipulated as well. With increasing Fermi energy, the energy band can be transformed from the allowed bands to the prohibited bands and then transformed along the opposite direction to the allowed bands. Because the conductivity changes rapidly in low frequency range, while changes slowly in high frequency range, as the Fermi energy increases, the energy band in the low frequency region will move quickly to higher frequency region, and the energy band in the high frequency region moves slowly, leading to the band compression and mutual conversion between the allowed and the prohibited bands. The larger the Fermi energy, the more obvious the band compression, and the more easy the mutual conversion.