A liquid crystal display includes a liquid crystal panel having a plurality of pixel units, a scanning driver configured to provide scanning signals to scan the pixel units, a data driver configured to provide data voltage signals to the pixel electrode of the pixel units; and a common voltage driver configured to provide a common voltage signal to the common electrodes of the pixel units. Each pixel unit includes a pixel electrode and a common electrode, and the pixel units cooperatively display picture frame by frame. A dummy cycle period is defined between two sequent normal frame periods. The common voltage signal is an alternating current voltage signal in each normal frame period, and a polarity of the common voltage signal is fixed in the dummy cycle. A method for driving a liquid crystal display is also provided.