This study analyzed the mechanical and fracture behavior of graphene/copper (Cu) composites with different Cu thicknesses by using molecular dynamics (MD) and representative volume element (RVE) analysis. Three graphene/Cu composite analytical models were classified as 4.8, 9.8, and 14.3 nm according to Cu thicknesses. Using MD analysis, zigzag-, armchair-, and z (thickness)-direction tensile analyses were performed for each model to analyze the effect of Cu thickness variation on graphene/Cu composite strength and delamination fracture. In the RVE analysis, the mechanical characteristics of the interface between graphene and Cu were evaluated by setting the volume fraction to 1.39, 2.04, and 4.16% of the graphene/Cu composite model, classified according to the Cu thickness. From their obtained results, whether the graphene bond is maintained has the greatest effect on the strength of graphene/Cu composites, regardless of the Cu thickness. Additionally, graphene/Cu composites are more vulnerable to armchair direction tensile forces with fracture strengths of 14.7, 8.9, and 8.2 GPa depending on the Cu thickness. The results of this study will contribute to the development of guidelines and performance evaluation standards for graphene/Cu composites.