Porous sheet-like structure of cuprous oxide powder composed of nano-size particles was successfully fabricated by solution combustion method and used as the precursors of copper to prepare the reduced graphene oxide/copper (rGO/Cu) composites. Graphene oxide (GO)/Cu2O hybrids were fabricated by mixing the as-prepared positively charged cuprous oxide colloid with negatively charged GO colloid with uniform distribution of GO by assistance of electrostatic interaction. The hybrids was reduced to rGO/Cu composite in H-2 atmosphere and followed by powder metallurgy to form rGO/Cu composite bulk. Microstructure studies indicated that the large-size rGO with 1wt% content were well and orderly distributed in copper matrix. Microhardness measurements and compression test showed considerable improvements in Vickers hardness from 48 to 58.3Hv accompanied by retaining the high conductivity of 90.63% IACS due to the addition of graphene. This method offers a new effective approach to fabricate rGO-reinforced copper composites.