The Cu-doped and undoped HfO2 films were fabricated by magnetron sputtering. The effect of Cu doping on resistive switching (RS) of HfO2 film was demonstrated. Improvements in ON/OFF ratio and switching parameters were observed. The multilevel behavior of Cu/HfO2:Cu/Si sample was also investigated by controlling the current compliance during set process and at least three low resistance states (LRSs) for data storage could be obtained. The three LRSs and the high resistance state can be distinguished in a range of 10(3) and the HfO2:Cu sample exhibited good reliability. The RS behavior of HfO2:Cu sample can be well interpreted by the proposed filamentary model. The oxygen vacancies and Cu ions in the film are both responsible for the RS behaviors.