A method and an apparatus for over-driving a liquid crystal display (LCD) are provided, which are suitable for compensating a gray level brightness of the LCD. The method includes the following steps. Firstly, a data buffer unit outputs a current frame data. Then, the current frame data is stored into a frame memory unit, and the frame memory unit outputs a previous frame data. Next, several look-up tables (LUTs) are searched for a driving voltage in a corresponding LUT according to the current frame data and the previous frame data. Afterward, a position scanning unit receives the current frame data to determine a current position. Finally, a multiplexer outputs the corresponding driving voltage at the current position. Thus, a display panel has the same gray level brightness in upper, middle, and lower portions thereof, thereby avoiding ghosting.