Nanoscaled room-temperature ferroelectricity is ideal for developing advanced non-volatile high-density memories. However, reaching the thin film limit in conventional ferroelectrics is a long-standing challenge due to the possible critical thickness effect. Van der Waals materials, thanks to their stable layered structure, saturate interfacial chemistry and weak interlayer couplings, are promising for exploring ultra-thin two-dimensional (2D) ferroelectrics and device applications. Here, we demonstrate a switchable room-temperature ferroelectric diode built upon a 2D ferroelectric {alpha}-In2Se3 layer as thin as 5 nm in the form of graphene/{alpha}-In2Se3 heterojunction. The intrinsic out-of-plane ferroelectricity of the {alpha}-In2Se3 thin layers is evidenced by the observation of reversible spontaneous electric polarization with a relative low coercive electric field of ~$2 X 10^5 V/cm$ and a typical ferroelectric domain size of around tens ${mu}m^2$. Owing to the out-of-plane ferroelectricity of the {alpha}-In2Se3 layer, the Schottky barrier at the graphene/{alpha}-In2Se3 interface can be effectively tuned by switching the electric polarization with an applied voltage, leading to a pronounced switchable double diode effect with an on/off ratio of ~$10^4$. Our results offer a new way for developing novel nanoelectronic devices based on 2D ferroelectrics.