We have studied the resistive switching (RS) phenomenon in series of BiFeO3 thin films of thickness of 40 – 154 nm deposited by PLD technique on conducting Nb-doped substrate of SrTiO3 and with Pt top electrodes. It was found that 154 nm film demonstrates the interface-provided I–V characteristic of Schottky diode when the applied voltage does not exceed the threshold value Vd = 1.3 V. The RS phenomenon appears as the current hysteresis loop during the 0 → Vm → 0 → −Vm → 0 voltage sweep cycle, provided that the maximal stop-voltage Vm is larger than Vd. For thinner films neither diode-like I–V behavior nor substantial RS effect were observed. The results are interpreted in terms of the filamentary model of the mobile oxygen vacancies.