An apparatus and method for driving an LCD device is provided. The apparatus for driving an LCD device comprises an image display unit that includes liquid crystal cells formed in each region defined by a plurality of gate lines and a plurality of data lines. A data driver supplies analog video signals to the respective data lines. A gate driver supplies scan pulses to the respective gate lines. A data converter detects motion vectors from input data and generating modulated data by filtering the input data in accordance with the motion vectors to generate overshoot or undershoot in a boundary along a motion direction. A timing controller aligns the modulated data to supply the aligned data to the data driver and operates the data driver and the gate driver.