Disclosed are a display apparatus and a method of driving the same. An image signal receiver sequentially outputs frames for image display. A local illumination calculation unit displays an image on a display unit based on the frames and calculates light emission amount of a light source provided for each section of a backlight unit. A frame interpolator generates sub-frames based on the frames and outputs the sub-frames and the frames. A pixel adjuster adjusts light transmittance of each pixel according to the brightness of each pixel and the amount of the light emitted from each section which is calculated by the local illumination calculation unit when the image is displayed based on the frames and the sub-frames sequentially output from a frame interpolator. Local illumination is realized without increasing the number of memory devices while a frame frequency is increased.