A liquid crystal display including a plurality of pixels includes a gray voltage generator generating a plurality of gray voltages, a data driver supplying data voltages selected from the gray voltages corresponding to image data to the pixels, a gate driver supplying gate voltages to gate lines of the pixels, a signal controller supplying a first control signal to the gate driver and the image data and a second control signal to the data driver for controlling the image data and comprising a dimming controller, the dimming controller generating a dimming signal based on an average gray of the image data over at least one frame and a common voltage generator generating at least one common voltage based on the dimming signal and applying the common voltage to the pixels. Therefore, the variation of the pixel voltage depending on the gray of the image data is decreased to improve image quality of the LCD.