A method of driving a liquid crystal display device includes multiplying a frame frequency of an inputted current frame to generate a multiplied odd-numbered frame and a multiplied even-numbered frame; determining whether said current frame is a still image frame or a dynamic image frame; detecting an edge area at which a motion blur occurs from the multiplied odd-numbered frame and the multiplied even-numbered frame; converting gray level values of pixels positioned at the detected edge area at the multiplied odd-numbered frame and the multiplied even-numbered frame; and continuously outputting the multiplied odd-numbered still image frame and the multiplied even-numbered still image frame or continuously outputting the multiplied odd-numbered dynamic image frame and the multiplied even-numbered dynamic image frame having the converted gray level values in accordance with the determined result. A liquid crystal display device is also disclosed.