An apparatus and method for driving an LCD device is provided. The apparatus includes an LCD panel that is comprised of red, green, blue and white sub-pixels. A data converter converts input data of three colors into input data of four colors. A data driver converts the input data of four colors into a video signal, and supplies the video signal to each sub-pixel. A gate driver supplies a scan pulse to each sub-pixel. A timing controller arranges the input data of four colors supplied from the data converter and then supplies the arranged data to the data driver. A backlight unit is comprised of LEDs of at least five colors to emit the light to the LCD panel. A backlight controller controls the backlight unit in accordance with the input data of three colors and the sub-frame control signal.