A liquid crystal display (LCD) and a driving method thereof are provided. The LCD comprises a liquid crystal panel having a gate line, a data line, and a pixel defined by the intersection of the gate line and the data line; a grayscale voltage generating unit for generating a grayscale voltage; a driving voltage generating unit for generating a gate off voltage, a positive polarity gate on voltage, and a negative polarity gate on voltage, wherein the negative polarity gate on voltage is lower than the positive polarity gate on voltage; a gate driving unit for supplying the gate line with at least one of the positive polarity gate on voltage and the negative polarity gate on voltage; a data driving unit for supplying the pixel with a data voltage, wherein the data driving unit is supplied with the grayscale voltage from the grayscale voltage generating unit; and a signal control unit for controlling the data driving unit so that a positive polarity data voltage and a negative polarity data voltage are alternately applied to the pixel, and for controlling the gate driving unit so that the positive polarity gate on voltage is applied to the pixel supplied with the positive polarity data voltage and the negative polarity gate on voltage is applied to the pixel supplied with the negative polarity data voltage. Accordingly, the degree of flicker and image sticking is reduced.