An apparatus and method for driving an LCD device is disclosed to obtain rapid response speed and to enhance picture quality, in which the apparatus includes a liquid crystal panel that includes liquid crystal cells formed in areas defined by gate and data lines; a gate driver that supplies a scan pulse to the gate lines; a timing controller that modulates source data supplied from the external to modulated data for a rapid response speed of liquid crystal cell, and generates discrimination signals by comparing source data of a current frame with uppermost and lowermost gray scales of source data based on whether source data of a current frame is the same as source data of a previous frame or not; and a data driver that converts the modulated data into a video signal by using a plurality of gamma voltages including a first modulation voltage that is higher than an maximum gamma voltage or a second modulation voltage that is lower than a minimum gamma voltage, and supplies the video signal to the data lines.