Recent experiments on layered {alpha}-In2Se3 have confirmed its room-temperature ferroelectricity under ambient condition. This observation renders {alpha}-In2Se3 an excellent platform for developing two-dimensional (2D) layered-material based electronics with nonvolatile functionality. In this letter, we demonstrate non-volatile memory effect in a hybrid 2D ferroelectric field effect transistor (FeFET) made of ultrathin {alpha}-In2Se3 and graphene. The resistance of graphene channel in the FeFET is tunable and retentive due to the electrostatic doping, which stems from the electric polarization of the ferroelectric {alpha}-In2Se3. The electronic logic bit can be represented and stored with different orientations of electric dipoles in the top-gate ferroelectric. The 2D FeFET can be randomly re-written over more than $10^5$ cycles without losing the non-volatility. Our approach demonstrates a protype of re-writable non-volatile memory with ferroelectricity in van de Waals 2D materials.
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