An image display apparatus and a method for operating the same are disclosed. The method for operating an image display apparatus includes receiving an image, separating the image into at least one of a two-dimensional (2D) image area or a three-dimensional (3D) image area, and displaying the at least one of the 2D or 3D image areas along with an area control object for changing a position or size of the 2D or 3D image area, on a display.