A liquid crystal display and a driving method thereof are provided. The liquid crystal display comprises a liquid crystal panel; a gate driver; a data driver; a timing controller supplying a control signal of the gate driver and a control signal of the data driver and supplying a brightness variable signal depending on an average of gray levels of image data; and a backlight unit adjusting a brightness level of the lamp in response to a plurality of brightness variable signals, wherein the timing controller divides the liquid crystal panel into a first division area, which displays image data, equal to or smaller than an average of reference gray levels and dispersion of reference gray levels and a second division area comprising areas other than the first division area by calculating an average and dispersion of gray levels of the image data with a line unit, and supplies a first brightness variable signal adjusting a brightness level of the first division area and a second brightness variable signal adjusting a brightness level of the second division area.