A method of driving a liquid crystal display device, which includes first and second substrates, gate lines on the first substrate, data lines crossing the gate lines to define pixel regions, a thin film transistor connected to each gate line and each data line, a common line between adjacent gate lines, a pixel electrode in each pixel region and overlapping the common line, and a common electrode on the second substrate, includes steps of sequentially applying scanning signals to the gate lines, applying data signals to the data lines to supply the pixel electrode with pixel voltage, applying a common voltage to the common electrode, and applying a storage capacitor voltage to the common line, wherein the pixel voltage and the storage capacitor voltage are alternating current (AC) voltages having positive and negative polarities alternately with respect to the common voltage.