An exemplary liquid crystal display (300) includes a liquid crystal panel (301) having a plurality of pixel units (340), a data processor (391) having a calculation circuit (393) and an analyzing circuit (394), and a common voltage circuit (305). The calculation circuit is configured to carry out a predetermined calculation between display signals corresponding to a current frame period and display signals corresponding to a previous frame period. The analyzing circuit is configured to provide a compensating signal according to a result of the calculation. The common voltage circuit is configured to adjust a reference voltage signal according to the compensating signal, so as to generate a common voltage signal for the pixel units. A related method for driving a liquid crystal display is also provided.