The described technology relates to a liquid crystal display and a driving method thereof. The liquid crystal display includes a plurality of pixels arranged in a matrix form. The pixels include a liquid crystal capacitor including a pixel electrode and a common electrode as two terminals. A plurality of data lines transfer data to the plurality of pixels. The pixels include a first pixel and a second pixel, which are adjacent to each other. First and second common signals are applied to the common electrode of the first and second pixels, respectively. The second common signal is inverted to the first common signal. The first and second common signals swing between a first voltage and a second voltage. The polarity of the data voltage transferred by a data line with respect to the first common signal or the second common signal is constant during one frame.