An autostereoscopic display and a control method thereof are disclosed. The autostereoscopic display includes a display panel displaying 3D image data, a backlight unit providing light to the display panel, a backlight driver which sequentially drives light sources of the backlight unit along a scanning direction of the 3D image data written to the display panel, a switchable 3D element which forms a barrier or a lens for separating optical axes of left eye image data and right eye image data from the 3D image data, and a 3D element driver which electrically controls the switchable 3D element and shifts the barrier or the lens formed in the switchable 3D element.