In a display apparatus and a driving method thereof, image data corresponding to plural different positions of a display panel are added to each other, and a sum of the image data of a present frame is compared with a sum of the image data of a previous frame to determine whether an image displayed on the display panel is a still image or not. While a still image is displayed, brightness of the display panel is gradually lowered. Accordingly, the display panel may prevent occurrence of afterimages and deterioration of organic electroluminescent light emitting devices, as well as reduce power consumption.