In a driving device, a liquid crystal display having the driving device, and a method of driving the liquid crystal display, the driving device includes a signal controller, a voltage selector, a gray-scale voltage generator, and a data driver. The signal controller outputs a power-down signal indicating an imminent power-off. The voltage selector outputs a common voltage in response to the signal. The gray-scale voltage generator receives the common voltage to generate common gray-scale voltages having a same voltage level as that of the common voltage. The data driver generates common data voltages based on the common gray-scale voltages. The driving device controls a display panel so that the display panel displays a white image in response to the signal. Thus, an after-image after the power-off is removed, therefore improving the display quality of the display panel.