Molecular dynamic simulations have been performed to investigate the effects of Cu {111}/graphene interface structures on the initial dislocation nucleation behavior in Cu/graphene layered composites. The characteristics of interfacial structures, including four possible types of stacking structures, interfacial misfit dislocations and interfacial energy distribution, have been studied based on geometrical analysis Thompson tetrahedron, disregistry analysis, and excess potential energy. In addition, interfacial structures are transformed by rotating the graphene layer with various angles, which further changing the morphology of the interface. After relaxation, the equilibrium state of the interface consists of a hexagon unit region arranging in periodicity, which also depicts the periodic energy distribution both on the Cu and graphene side. Under uniaxial X and Y directions loading, the evolution of interface patterns provides a non-Schmid factor for initial interfacial dislocation nucleation which prefers to locate the sites of higher potential energy area. Moreover, the rotation of the graphene layer changes the interfacial structures by changing the atoms mismatch on the Cu/graphene interface, which consequently influences the nucleation conditions including sites, morphology and slip system as well. This work provides an understanding of the Cu/graphene interface-dominated dislocation nucleation.