A liquid crystal display device and a driving method thereof are provided. The liquid crystal display includes a data driver that is operative to supply data to the data lines. The data have the same polarity for the liquid crystal cells that are adjacent horizontally and opposite polarities for the liquid crystal cells that are adjacent vertically. A gate driver is operative to supply scan signals to the gate lines. The scan signals have different swing widths from each other in accordance with a polarity of the data. The switch devices include a plurality of first switch devices and a plurality of second switch devices. The first switch devices are connected to the (n−1)th (where n is a positive integer of not less than 2) gate line and the second switch devices are connected to the nth gate line.