In this paper, a novel composite is constructed as a non-enzymatic hydrogen peroxide (H2O2) sensor by liquid-phase exfoliation method, which is composed of copper oxide, cuprous oxide and silver nanoparticles doped few-layer-graphene (CuxO/Ag@FLG). Its surface morphology and composition were characterized by scanning electron microscopy (SEM) and X-ray photo spectroscopy (XPS), and its H2O2 sensing performances include catalytic reduction and quantitative detection were studied with electrochemical methods. Our sensor had a high sensitivity of 174.5 μA mM−1 cm−2 (R2 = 0.9978) in an extremely wide range of concentrations from 10 μM to 100 mM, a fast response (about 5 s) and a low limit of detection (S/N = 3) of 2.13 μM. The sensor exhibits outstanding selectivity in the presence of various biological interference, such as dopamine, ascorbic acid, uric acid, citric acid, etc. In addition, the constructed sensor continued 95% current responsiveness after 1 month of storage further points to its long-term stability. Last but not least, it has a good recovery rate (90.12–102.00%) in milk sold on the open market, indicating that it has broad application possibilities in the food industry and biological medicine.