Clear understanding the mechanism of resistive switching is the important prerequisite for the realization of high performance nonvolatile resistive random access memory. In this paper, binary metal oxide MoOx layer sandwiched by ITO and Pt electrodes was taken as a model system, reversible transition of abnormal and normal bipolar resistive switching (BRS) in dependence on the maximum voltage was observed. At room temperature, below a critical maximum voltage of 2.6 V, butterfly shaped I-V curves of abnormal BRS has been observed with low resistance state (LRS) to high resistance state (HRS) transition in both polarities and always LRS at zero field. Above 2.6 V, normal BRS was observed, and HRS to LRS transition happened with increasing negative voltage applied. Temperature dependent I-V measurements showed that the critical maximum voltage increased with decreasing temperature, suggesting the thermal activated motion of oxygen vacancies. Abnormal BRS has been explained by the partial compensation of electric field from the induced dipoles opposite to the applied voltage, which has been demonstrated by the clear amplitude-voltage and phase-voltage hysteresis loops observed by piezoelectric force microscopy. The normal BRS was due to the barrier modification at Pt/MoOx interface by the accumulation and depletion of oxygen vacancies.