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In this study, a sensor for the detection of glucose and hydrogen peroxide was developed on the basis of Cu2O nanocubes wrapped by graphene nanosheets (Cu2O/GNs) as electrocatalysts. Cubic Cu2O nanocrystals/graphene hybrid has been successfully fabricated by a chemical reduction method at low temperature. The morphologies of the synthesized materials were characterized by scanning electron microscopy (SEM) and powder X-ray diffraction measurements (XRD). As a non-enzymatic amperometric sensor, the resulting Cu2O/graphene composite exhibited high sensitivity for the detection of glucose and H2O2 . Moreover, the graphene coating was found to be able to effectively improve the electrochemical cycling stability of the fabricated sensor. With the Cu2O/GNs modified electrode, amperometric sensing of glucose was realized with a linear response over the concentration range from 0.3 to 3.3 mM, a detection limit of 3.3 m M (S/N=3), high selectivity and short response time (<9 s). Compared to unsupported Cu2O nanocubes, the graphene-wrapped Cu2O nanocubes exhibited higher catalytic activity for glucose oxidation with higher sensitivity and lower detection limit. The enzymeless sensor also exhibited good response toward H2O2 , with the linear response ranging from 0.3 to 7.8 mM at -0.4 V and the detection limit of 20.8 m M. Moreover, because the surface is covered by graphene nanosheets, the as-synthesized Cu2O/GNs exhibited improved electrochemical stability. Such novel graphene nanosheets wrapped Cu2O nanocubes represent promising enzyme-free glucose and hydrogen peroxide sensors with high sensitivity and selectivity, improved stability and fast amperometric response.