In this paper, the resistive switching characteristics of Ag/BiFeO₃/Fe₂O₃/ITO multilayer film deposited on ITO by magnetron sputtering are investigated. The Ag/BiFeO₃/Fe₂O₃/ITO devices all exhibit superior resistive switching behaviors due to the formation of Ag conducting filaments. The resistive switching ratio of the device is close to 10 for the sample with 100nm-thick Fe₂O₃ film. The current value of the device increases sharply at 0.56 V when the voltage is swept forward, and the device switches from LRS back to HRS at –0.3 V when a voltage of opposite polarity is applied. The I-V curves of the device are fitted in double logarithmic coordinates. It is found that the device is controlled by an Ohmic conduction model in the low resistance state and by two conduction models in the high resistance state: Ohmic conduction in the low bias region, and the SCLC conduction model at higher voltages. Such a resistive switching characteristic with very low switching voltage and a high resistance ratio is particularly important for the application of resistive stochastic storage. In addition, all samples show an obvious negative differential resistance effect, which is caused by Joule heating. The Ag/BiFeO₃/Fe₂O₃/ITO device show both resistive switching characteristics and a negative differential resistance effect, which have important applications.