In this paper, a WO3-based resistive random access memory device composed of a thin film of WO3 sandwiched between a copper top and a platinum bottom electrodes is fabricated by electron beam evaporation at room temperature. The reproducible resistive switching, low power consumption, multilevel storage possibility, and good data retention characteristics demonstrate that the Cu/WO3/Pt memory device is very promising for future nonvolatile memory applications. The formation and rupture of localised conductive filaments is suggested to be responsible for the observed resistive switching behaviours.