A liquid crystal display for changing a supply sequence of a scanning pulse with which a plurality of gate lines are supplied to realize a one dot inversion, and a driving method thereof are disclosed.In the liquid crystal display, a liquid crystal display panel has a plurality of data lines and a plurality of gate lines, which are crossed each other, and pixels, which are defined by the lines. A gate driver supplies scanning pulses to the gate lines, and changes a supply sequence of the scanning pulses for each frame. A data driver converts digital video data into data voltages and periodically inverts a polarity of the data voltages to supply the data voltages in accordance with a supply sequence of the scanning pulses. And a timing controller supplies the digital video data to the data driver, and controls the data driver and the gate driver, and wherein a polarity of data voltages, which are supplied to the liquid crystal display panel, is inverted for each liquid crystal cell and a polarity of a data voltage which is outputted from the data driver, is inverted for every two to four horizontal periods.