Resistive switching memories have attracted considerable attention for their potential applications in next-generation nonvolatile memory devices due to high switching speed, high volume storage, low power consumption, and non-destructive readout. In this paper, a controllable and nonvolatile rewritable bipolar organic memory based on the active poly(o-methoxyaniline) (POMA) film is demonstrated. The capacitive device structure of Al/POMA/ITO exhibits good bistable resistive switching characteristics with a high ON/OFF current ratio of ~103, low switching voltage, good cycling endurance, and long retention time of over 104s. The observed bipolar switching phenomena could be elucidated by the formation and annihilation of conductive filaments, which corresponded to oxidation and reduction of metal Al top electrode and/or POMA polymer molecule chains.