A liquid crystal display, apparatus for driving a liquid crystal display and a method of driving gray voltages for the same. The liquid crystal display includes a plurality of gate lines transmitting gate signals, a plurality of data lines intersecting the plurality of gate lines and transmitting data voltages, and a plurality of pixel rows. Each pixel row includes a plurality of pixels, and each pixel includes a switching element connected to one of the plurality of gate lines and one of the plurality of data lines. The polarity of the data voltages supplied to the plurality of pixels are inverted by a pixel group including two or more pixel rows. The absolute values of the data voltages applied to one row of the pixel group with respect to a first predetermined voltage are greater than the absolute values of the data voltages applied to another row of the pixel group for the same grays.