Organic nonvolatile memory devices have a vital role for the next generation of electrical memory units, due to their large scalability and low-cost fabrication techniques. Here, we show bipolar resistive switching based on an Ag/ZnO/P3HT-PCBM/ITO device in which P3HT-PCBM acts as an organic heterojunction with inorganic ZnO protective layer. The prepared memory device has consistent DC endurance (500 cycles), retention properties (104 s), high ON/OFF ratio (105), and environmental stability. The observation of bipolar resistive switching is attributed to creation and rupture of the Ag filament. In addition, our conductive bridge random access memory (CBRAM) device has adequate regulation of the current compliance leads to multilevel resistive switching of a high data density storage.