Graphene has attracted much interest in many scientific fields because of its high specific surface area, Young's modulus, fracture strength, carrier mobility and thermal conductivity. In particular, the graphene oxide (GO) prepared by chemical exfoliation of graphite has achieved low-cost and large-scale production and is one of the most promising for Cu matrix composites. Here, we prepared a high strength, high electrical conductivity and high thermal conductivity reduced graphene oxide (RGO)/Cu composite by directly heating the GO/copper formate. The oxygen-containing functional groups and defects of RGO are significantly reduced compared with those of GO. The tensile yield strength and thermal conductivity of RGO/Cu composite with RGO volume fraction of 0.49 vol.% are as high as 553 MPa and 364 W/(m·K) at room temperature, respectively. The theoretical value of the tensile yield strength of the composite is calculated according to the strengthening mechanism, and the result shows that it agrees with the experimental value. After hot-rolling treatment, the ductility and conductivity of the composite materials have been greatly improved, and the ductility of the RGO/Cu composite with RGO volume fraction of 0.49 vol.% has been increased to four times the original. This work provides a highly efficient way to fabricate a high-performance RGO-reinforced Cu composite for commercial application.