A numerical simulation was introduce to investigate the memory effect due to the current bistability resulting from the existence of the traps in organic memory devices with a single active layer. The drift-diffusion model together with a field dependent mobility model and single level trap model was used to simulate the current bistability. The currents at the same reading voltage under various writing voltages were significantly larger than that without a writing voltage. The electric field induced by the trapped electrons near the electrode increased the device current, resulting in appearance of the current bistability in the device. These simulation results can help to improve understanding of the theoretical current bistability in organic memories.