Liquid crystal display and driving method thereof

A liquid crystal display includes a liquid crystal display panel including a plurality of data lines, a plurality of gate lines crossing the plurality of data lines, and a plurality of liquid crystal cells, a timing controller to determine gray levels of input digital video data and a time when a polarity of a data voltage to be supplied to the data lines is inverted, and to generate a dynamic charge share control signal when the gray level of the data voltage is changed from a white gray level to a black gray level and the polarity of the data voltage is inverted, a data driving circuit to convert the digital video data from the timing controller into the data voltage, changing the polarity of the data voltage, and supplying any one of a common voltage and a charge share voltage to the data lines in response to the dynamic charge share control signal, and a gate driving circuit to sequentially supply scan pulses to the gate lines under the control of the timing controller.