A detailed understanding of interactions between molecules and graphene is one of the key issues for tailoring the properties of graphene-based molecular devices, because the electronic and structural properties of molecular layers on surfaces are determined by intermolecular and molecule-substrate interactions. Here, we present the atomically resolved experimental measurements of the self-assembled fullerene molecules on single-layer graphene on Cu(111). Fullerene molecules form a (4 × 4) superstructure on graphene/Cu(111), revealing only single molecular orientation. We can resolve the exact adsorption site and the configuration of fullerene by means of low-temperature scanning tunnelling microscopy (LT-STM) and density functional theory (DFT) calculations. The adsorption orientation can be explained in terms of the competition between intermolecular interactions and molecule-substrate interactions, where strong Coulomb interactions among the fullerenes determine the in-plane orientation of the fullerene. Our results provide important implications for developing carbon-based organic devices using a graphene template in the future.