The Ce and Mn co-doped BiFeO3 (BCFMO) thin films were synthesized on Pt/Ti/SiO2/Si substrates using a sol-gel method. The unipolar resistive switching (URS) and bipolar resistive switching (BRS) behaviors were observed in the Pt/BCFMO/Pt device structure, which was attributed to the formation/rupture of metal filaments. The fabricated device exhibits a large ROFF/RON ratio (>80), long retention time (>105 s) and low programming voltages (<1.5 V). Analysis of linear fitting current-voltage curves suggests that the space charge limited leakage current (SCLC) and Schottky emission were observed as the conduction mechanisms of the devices.