There provides a liquid crystal display and a data driver thereof. The data driver includes: an output module for outputting N groups of data voltage sets to N groups of data line sets; and N selection modules, each one corresponding to one group of data voltage set and one group of data line set; wherein each selection module selects data voltages of the corresponding group of data voltage set to provide to data lines in the corresponding group of data line set according to different control signals when the liquid crystal display drives pixels in different polarity reversal manners. The liquid crystal display and the data driver thereof in the present invention may achieve the goal of free switching between the single-point polarity reversal manner and the double-point polarity reversal manner.