Current-voltage hysteresis and switchable rectifying characteristics have been observed in epitaxial multiferroic BiFeO3 (BFO) thin films. The forward direction of the rectifying current can be reversed repeatedly with polarization switching, indicating a switchable diode effect and large ferroelectric resistive switching. With analyzing the potential barriers and their variation with ferroelectric switching at the interfaces between the metallic electrodes and the semiconducting BFO, the switchable diode effect can be explained qualitatively by the polarization-modulated Schottky-like barriers.