A two dimensional/three dimensional (2D/3D) switchable autostereoscopic display apparatus and method to selectively display a 2D image and a 3D image using two displays and a convertible lens. When outputting the 2D image, the 2D/3D switchable autostereoscopic display apparatus may control a first display to output a white image/white light, control a second display to output an image, and control an electrical diffuser lens of the convertible lens to be switched off and the white image to be diffused so as to operate as a backlight. When outputting the 3D image, the 2D/3D switchable autostereoscopic display apparatus may control the first display to output an image, control the second display to be switched off to be in a transparent state, control the electrical diffuser lens of the convertible lens to be switched on to be in the transparent state, and control the lenticular lens to output the 3D image.