SiO2 thin films were fabricated as resistive layers of Cu/SiO2/Pt devices to investigate resistive switching properties. A thermal annealing was performed to allow for the diffusion of Cu ions into the SiO2 thin films, leading to the formation of Cu-doped SiO2 layers. Occurrence probabilities of the resistive switching and initial resistance-states of the devices were influenced by SiO2 thickness, which was dependent on the Cu diffusion status within the SiO2 layer. The resistive switching behaviors were characterized by the voltage sweeping mode and the current sweeping mode. The current sweeping mode provided a desired compliance current to well control the resistive switching from the high resistance-state to the low resistance-state (SET). Therefore, the large RESET (from the low resistance-state to the high resistance-state) current was not inherent in the device, due to poor control of the compliance current by the voltage sweeping mode. The current sweeping mode is a simple method to characterize the RESET current.