disclosed is a liquid crystal display and a method for driving the same . in the method , the data voltage representing image signals are applied to a plurality of pixels arranged in columns and rows , and the polarity of the data voltage for common voltage inverts the pixel groups comprised of two or more pixels . the inventive lcd includes a substrate , a plurality of gate lines formed on the substrate , a plurality of data lines insulated from and intersecting the gate lines , and a plurality pixels formed corresponding to respective regions defined by the data lines and gate lines . common voltage is applied to the plurality of pixels , and the polarity of the data voltage for the common voltage inverts in units of pixel groups comprised of two or more pixels .