Two-dimensional (2D) ferroelectrics has emerged as a promising building block for nonvolatile memory devices. In this work, we demonstrate the out-of-plane ferroelectricity of 2D CuCrP2S6 (CCPS) at the room temperature and the switchable diode effect in 2D CCPS-based ferroelectric nanodevices. The spontaneous out-of-plane ferroelectric polarization switching and hysteresis loops are directly evidenced by the piezoresponse force microscopy. The intrinsic ferroelectricity originates from the non-centrosymmetric structure of 2D CCPS, which is confirmed by optical second-harmonic generation technique. A ferroelectric tunnel junction was built up by using 2D CCPS as a function layer. The observed diode-like forward rectification effect of CCPS diode is opposite to the direction of remnant polarization, which is attributed to the ferroelectric polarization modulation of Schottky barrier. Our work highlights the great potential of 2D CCPS in ultrathin ferroelectric memory device and motivates the development of multifunctional nanodevices.