Graphene with ultrahigh intrinsic strength and excellent thermal physical properties has the potential to be used as the reinforcement of many kinds of composites. Here, we show that very high tensile strength can be obtained in the copper matrix composite reinforced by reduced graphene oxide (RGO) when micro-layered structure is achieved. RGO-Cu powder with micro-layered structure is fabricated from the reduction of the micro-layered graphene oxide (GO) and Cu(OH) composite sheets, and RGO-Cu composites are sintered by spark plasma sintering process. The tensile strength of the 5 vol.% RGO-Cu composite is as high as 608 MPa, which is more than three times higher than that of the Cu matrix. The apparent strengthening efficiency of RGO in the 2.5 vol.% RGO-Cu composite is as high as 110, even higher than that of carbon nanotube, multilayer graphene, carbon nano fiber and RGO in the copper matrix composites produced by conventional MLM method. The excellent tensile and compressive strengths, high hardness and good electrical conductivity are obtained simultaneously in the RGO-Cu composites. The results shown in the present study provide an effective method to design graphene based composites with layered structure and high performance.