In this work, we demonstrate the fabrication of a unique hybrid structure by directly growing ultrathin Cu2O nanowires (about 5nm in diameter) onto reduced graphene oxide (rGO) sheets via a facile solvothermal method. This is a facile process carried out at 120 degrees C for 6h, in which only cupric acetate and rGO sheets are used as initiating materials, ethylene glycol as the solvent and reducing agent, and soldium acetate as precipitator, without employing any additional surfactant. Furthermore, the as-obtained nanocomposites-modified glassy carbon electrode (GCE) shows significantly improved electrochemical performance in nonenzymatic amperometric glucose detection, exhibiting the good linear behavior with glucose concentrations ranging from 10M to 0.1mM with a high gradient of 80.17A/mM. More importantly, interference from the oxidation of common interfering species under physiological conditions, such as uric acid, dopamine, and ascorbic acid, is effectively avoided. Therefore, these nanocomposites may be a promising electrode material for the determination of glucose.