The extraordinary strength of metal/graphene composites is significantly determined by the characteristic size, distribution and morphology of graphene. However, the effect of the graphene size/distribution on the mechanical properties and related strengthening mechanisms has not been fully elucidated. Herein, under the same volume fraction and distribution conditions of graphene, molecular dynamics simulations were used to investigate the effect of graphene sheet size on the hardness and deformation behavior of Cu/graphene composites under complex stress field. Two models of pure single crystalline Cu and graphene fully covered Cu matrix composite were constructed for comparison. The results show that the strengthening effect changes with varying the graphene sheet size. Besides the graphene dislocation blocking effect and the load-bearing effect, the deformation mechanisms change from stacking fault tetrahedron, dislocation bypassing and dislocation cutting to dislocation nucleation in turn with decreasing the graphene sheet size. The hardness of Cu/graphene composite, with the graphene sheet not completely covering the metal matrix, can even be higher than that of the fully covered composite. The extra strengthening mechanisms of dislocation bypassing mechanism and the stacking fault tetrahedra pinning dislocation mechanism contribute to the increase in hardness.