A display apparatus which outputs a stereoscopic image and a control method thereof, the display apparatus includes: an image input part which receives left and right eye image frames; an image processor which generates a left eye image interpolation frame by using a gradation difference of areas between a previous right eye image frame of the left eye image frame and the left eye image frame and generates a right eye image interpolation frame by using a gradation difference of areas between a previous left eye image frame of the right eye image frame and the right eye image frame; a display which displays the left eye image interpolation frame, the left eye image frame, the right eye image interpolation frame, and the right eye image frame sequentially according to a preset order; and a controller which controls the image processor to generate the left and right eye image interpolation frames.