The synergy between mechanical strength and ductility as well as electrical conductivity (EC) is of great importance for the application of Cu matrix composites (CMCs). In this work, a Cu@reduced graphene oxide (RGO) core-shell structure was purposively constructed to prepare RGO/Cu composites. The results show that this core-shell structure prepared by electrostatic adsorption and chemical reduction is beneficial to the uniform distribution of RGO and the formation of Cu-O-C bonds at the RGO/Cu interface. Compared with pure Cu, the yield strength (YS) and ultimate tensile strength (UTS) of the RGO/Cu composite with only 1% RGO are improved by 119% and 40%, respectively. While it maintains high ductility and EC, almost consistent with that of pure Cu. The core-shell structure enhances the load transfer efficiency of the RGO/Cu interface, and reduces the interfacial obstruction of electron transport. This work achieves a good balance of mechanical strengthening and electrical conducting, which provides a new strategy for the development of graphene/Cu composites.