Hybrid systems consisting of graphene and various two-dimensional materials would provide more opportunities for achieving desired electronic and optoelectronic properties. Here, we focus on a superlattice composed of graphene and monolayer MoS2. The geometric and electronic structures of the superlattice have been studied by using density functional theory. The possible stacking models, which are classified into four types, are considered. Our results revealed that all the models of graphene/MoS2 superlattices exhibit metallic electronic properties. Small band gaps are opened up at the K-point of the Brillouin zone for all the four structural models. Furthermore, a small amount of charge transfer from the graphene layer to the intermediate region of C–S layers is found. The band structure and the charge transfer together with the buckling distortion of the graphene layer in the superlattice indicate that the interaction between the stacking sheets in the superlattice is more than just the van der Waals interaction.