An apparatus for driving an LCD device includes an image display unit having liquid crystal cells in respective regions defined by a plurality of gate and data lines; an over-driving apparatus to detect a signal of a moving image based on a source data and to detect modulated data based on the detected signal, the modulated data changes a response speed of a liquid crystal based on the detected signal; a gate driver to supply scan signals to the gate lines; a data driver to convert the modulated data into analog video signals and to supply the analog video signals to the data lines; and a timing controller to align the modulated data and to generate data control signal and gate control signal, the timing controller outputs the aligned data and the data control signal to the data driver and outputs the gate control signal to the gate driver.