A novel, stable and sensitive non-enzymatic glucose sensor was developed by potentiostatically electrodepositing metallic Cu nanoparticles on graphene sheets. The electrochemical performance of the Cu-graphene sheets electrode for detection of glucose was investigated by cyclic voltammetry and chronamperometry. The Cu-graphene sheets electrode displayed a synergistic effect of copper nanoparticles and graphene sheets towards the oxidation of glucose in alkaline solution, showing higher oxidation current and negative shift in peak potential. At detection potential of 500 mV, the Cu-graphene electrode sensor presented a wide linear range up to 4.5mM glucose with a detection limit of 0.5 μM (signal/noise=3). In addition, the sensor responds very quickly (<2s) with addition of glucose. Furthermore, the Cu-graphene sheets electrode exhibits high stability and selectivity to glucose, and the poisoning by chloride ion as well as interference from the oxidation of common interfering species (ascorbic, dopamine, uric acid and carbohydrate) are effectively avoided. The Cu-graphene sheets electrode allows highly selective and sensitive, stable and fast amperometric sensing of glucose, which is promising for the development of non-enzymatic glucose sensor.