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The effect of operation current on the high-resistance state and the endurance for the HfOx-based resistive device is comprehensively studied. Due to the current overshoot by the parasitic capacitances, an excess current leakage for the high resistance state of the 1R device after the forming and SET stages is observed. The accelerated degradation of the high-resistance state for the HfOx device undergoing a high-operation-current stage is revealed for the first time. As the compliance current increases beyond 500 μA, the resistance of the high-resistance state of the device deceases drastically. A possible scenario about the correlation between the high-resistance state and the compliance current based on the filament model is proposed. By suppressing the current overshoot with the 1T1R device, the high-resistance state (>; 1 MΩ) and excellent endurance (>; 108 cycles) for the HfOx resistive memory are demonstrated.