An apparatus and method for driving an LCD device is disclosed, in which resolution of images can be improved by the difference in gray level between adjacent pixels of video data. The apparatus for driving an LCD device includes an LCD panel having a plurality of gate lines and a plurality of data lines, a data converter analyzing the difference in gray level between adjacent pixels of input video data and outputting modulated video data if the difference of gray level between adjacent pixels is larger than a reference value, a timing controller aligning and outputting the modulated video data, a gate driver supplying scan pulses to the gate lines of the LCD panel, and a data driver supplying the modulated video data to the data lines of the LCD panel.