Water vapor condensation is a key process for many applications. Existing studies in water vapor heterogeneous condensation have used different methods to modify the hydrophobicity of the water vapor condensation surface. One way to modify the surface properties is to use graphene coating. On a macroscale, surface modification using graphene coating can improve water vapor condensation heat transfer of various substrates. However, on the molecular scale, its effect is poorly understood. This work investigated the effect of graphene coating on water vapor condensation using molecular dynamics simulations (MDS). We examined the water vapor condensation on bare copper surfaces considering the effects of initial temperature difference, water model, and surface size, parameters that have not been investigated by previous studies employing MDS for the same water-surface configuration. One water model was then used to simulate the condensation on a copper surface with and without graphene coating. We then investigated the effect of graphene defect, the energy and vibration of graphene atoms, and the interaction between graphene and copper layers. The surface size notably influenced the condensation rate and heat transfer performance. The condensation rate and heat transfer performance were significantly reduced when the copper surface was coated by graphene. The number of water molecules condensed was 1253 molecules/ns on the bare copper surface, compared to 587 molecules/ns on the graphene-coated copper surface. Moreover, the water molecules condensed on the graphene-coated copper surface tended to return to the bulk vapor phase. Other important results are also provided. This study gives an insight into the water vapor condensation on graphene-coated copper surfaces, useful to pursuit the design and optimization of graphene-coated copper surfaces for applications that need efficient water vapor condensation, such as for industrial applications, like thermal, chemical, and nuclear.