The invention relates to a data driver of using a gamma selection signal and a flat panel display and a driving method thereof. A first left sub-pixel, a first right sub-pixel, a second right pixel and a second left sub-pixel are electrically connected with a first data line, a second data line, a third data line and a fourth data line respectively. The data driver comprises gray scale voltage generating units from first to fourth for respectively outputting a first group of positive gray scale voltage, a second group of negative gray scale voltage, a second group of positive gray scale voltage and a first group of negative gray scale voltage. The data driver drives the sub-pixels according to the first group of positive gray scale voltage, the second group of negative gray scale voltage, the second group of positive gray scale voltage and the first group of negative gray scale voltage under the control of a polarity inversion signal and the gamma selection signal.