An LCD and a driving method thereof include: data writing for applying a common voltage and a data voltage to a plurality of pixels; and sustaining for applying a shifted common voltage shifted by a predetermined level from the common voltage to the plurality of pixels for a sustain period during which the plurality of pixels emit light, corresponding to the data voltage. The shifted common voltage is shifted to an opposite polarity of a polarity of a gate-off voltage applied to the plurality of pixels to float the plurality of pixels. During a sustain period, a gate-source voltage of the switching transistor can be increased, and accordingly an influence due to the leakage current can be minimized, thereby preventing image deterioration. Further, since capacitance of the sustain capacitor can be reduced so that power consumption of the LCD can be reduced.