In a method for driving a liquid crystal display, a plurality of first enabling pulses are transmitted to a first group of scan lines in a first period of a predetermined time, respectively. A plurality of second enabling pulses are transmitted to a second group of scan lines in a second period of the predetermined time, respectively. The pixel voltages of pixel units, which are connected to the scan lines of the first and second group, are different in their polarities. During the predetermined time, a common voltage signal, which has different levels in the first and second period, is transmitted to the common line. A liquid crystal display applying the above driving method is also disclosed.