A stereoscopic display for switching between a 2D image and a 3D image, including a display device displaying an image; and a parallax barrier that transmits incident light in a 2D mode and forms barriers to separate images for a left eye and a right eye in a 3D mode. The parallax barrier unit includes a first polarization plate transmitting light with a first polarization direction; a 2D first polarization grating screen including a first birefringence element and a second birefringence element alternating with each other in a grating pattern; a 2D second polarization grating screen facing the first polarization grating screen and including a third birefringence element and a fourth birefringence element alternating with each other in a grating pattern; and a second polarization plate facing the second polarization grating screen and transmitting only light with a second polarization direction among lights transmitted through the second polarization grating screen.