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 silver, copper oxide and cuprous oxide-doped a few layers graphene (CuxO/Ag@FLG). Its surface morphology and composition are analyzed by scanning electron microscopy (SEM) and X-ray photo spectroscopy (XPS), and its H2O2 sensing performance include catalytic reduction and quantitative detection is studied with electrochemical method. Our sensor had a high sensitivity of about 1272.62 μA mM-1 cm-2 (R2=0.9923) in a extremely wide range of concentrations from 10 μM to 20 mM H2O2, a fast response (about 5 s) and 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 one month of storage further points to its long-term stability. Last but not least, it has a good recovery rate in the milk sold on the open market, indicating that it has a wide range of application possibilities in the food industry and biological medicine.