Precise switchover of numerous resistance states is desirable to achieve repeatable multilevel data storage memory windows. However, this could be hindered by the inherent random nature of oxygen vacancy creation. In this study, oxygen-deficient CeO2-x thin films were fabricated on indium tin oxide (ITO)-coated/glass substrates using radio-frequency magnetron sputtering at room temperature to obtain simple Ni/CeO2-x/ITO/glass devices. Multilevel bipolar resistive switching characteristics were investigated by controlling the RESET voltage and current compliance. The device could be regarded as four-level switching memory, controlled by the RESET voltage. An increase in the RESET-stop voltage from -1.5 to -2.0 V increased the Schottky barrier height, leading to an improvement in the ON/OFF ratio. The multilevel resistive switching behavior could be attributed to the formation and partial rupture of conductive filaments owing to interfacial oxygen ion migration. This study shows the potentials of the Ni/CeO2-x/ITO/glass devices for multilevel data storage resistive random-access memory applications.