A liquid crystal display device and a driving method thereof are disclosed. The method for driving the liquid crystal display device comprises the following steps: converting three primary color gray-scale data of a frame image to be displayed into multiple color gray-scale data; and driving different sub pixels according to the overdrive gray-scale values that are obtained through inquiring the overdrive table based on the multiple color gray-scale data of the frame image to be displayed according to a certain time sequence in two color fields. According to the method, the color shift phenomena of the traditional liquid crystal display device can be alleviated effectively.