Piezoelectric and ferroelectric properties in the two dimensional (2D) limit are highly desired for nanoelectronic, electromechanical, and optoelectronic applications. Here we report the first experimental evidence of out-of-plane piezoelectricity and ferroelectricity in van der Waals layered α-In2Se3 nano-flakes. The non-centrosymmetric R3m symmetry of the α-In2Se3 samples is confirmed by scanning transmission electron microscopy, second-harmonic generation, and Raman spectroscopy measurements. Domains with opposite polarizations are visualized by piezo-response force microscopy. Single-point poling experiments suggest that the polarization is potentially switchable for α-In2Se3 nano-flakes with thicknesses down to ~ 10 nm. The piezotronic effect is demonstrated in two-terminal devices, where the Schottky barrier can be modulated by the strain-induced piezopotential. Our work on polar α-In2Se3, one of the model 2D piezoelectrics and ferroelectrics with simple crystal structures, shows its great potential in electronic and photonic applications.