We have developed a non-enzymatic glucose sensor by using a composite prepared from copper nanoparticles (CuNPs) and graphene which can be prepared by simple 1-step electrochemical reduction using graphene oxide (GO) and copper ion as the starting materials. The GO is electrochemically reduced to graphene at a voltage of −1.5 V, and this is accompanied by the simultaneous formation of CuNPs on the surface of the graphene. This novel nanocomposite combines the advantages of graphene and of CuNPs and displays good electrocatalytic activity toward glucose in alkaline media. The performance of the respective glucose electrode was evaluated by amperometric experiments and revealed a fast response (<2 s), a low detection limit (200 nM), and high sensitivity (607 μA mM −1 ). The sensor also exhibits good reproducibility and very good specificity for glucose over ascorbic acid, dopamine, uric acid, fructose, lactose and sucrose.