In a two-dimensional/three-dimensional (2D/3D) switchable image display apparatus and a method of displaying 2D and 3D images, the 2D/3D switchable image display apparatus may comprise: a data driver which outputs column data of an input image; a scan driver which controls a driving method of a plurality of odd scan lines and a plurality of even scan lines according to an input method and a display mode of the input image; a display panel which displays a 2D image or a 3D image by separately displaying the input image in odd lines and even lines; and a parallax device which generates binocular parallax between an image displayed in the odd lines and an image displayed in the even lines.