We have fabricated a ferroelectric resistive switching device of Pt/Bi1-δFeO3 (BFO)/SrRuO3 (SRO) in which the conductivity of BFO layer was controlled by changing the Bi-deficiency concentration. The devices showed a bipolar-type resistive switching effect, i.e., zero-crossing hysteretic current–voltage (I–V) characteristics. In addition, the I–V characteristics in both high and low resistance states are nonlinear, which can avoid a read-error problem in a passive crossbar memory array. Resistive switching characteristics measured in pulse-voltage mode revealed that the resistance values in low resistance states vary with the amplitude and duration time of the pulsed-voltage stresses, indicating possibility of multilevel switching. On the basis of the experimental results, we discuss the potential of the Pt/BFO/SRO device for application in a large-capacity nonvolatile memory.