A 2D/3D switchable stereoscopic display which can provide a 3D image with complete parallax using two polarization grating screens is provided. The 2D/3D switchable stereoscopic display includes a display device which an image and a parallax barrier unit including first and second polarization grating screens facing each other. The parallax barrier unit has a 2D mode and a 3D mode and is switched between the 2D mode and the 3D mode when the two polarization grating screens are moved relative to each other. In the 2D mode, the parallax barrier unit transmits all light, and in the 3D mode, it forms a barrier and a plurality of apertures which are arranged at predetermined intervals in two dimensions, thereby transmitting light through only the apertures and thus providing a 3D image with horizontal parallax and vertical parallax.