An apparatus and method for driving a liquid crystal display (LCD) device is disclosed, to prevent error of a timing controller and to prevent the defective image on a frequency conversion, the apparatus comprising a liquid crystal display part to display images, a driver to drive the liquid crystal display part, a graphic system to output frequency-conversion prediction information in accordance with a frequency-conversion signal, and perform frequency conversion of a plurality of synchronizing signals, and a timing controller to control the driver to display video data according to a previous frame during the frequency conversion, in response to the frequency-conversion prediction information.