A liquid crystal display and method for driving the same to prevent a repaired pixel from being a bright spot. The LCD panel includes a plurality of pixels, each pixel including: a pixel capacitor, a storage capacitor, and a thin film transistor (TFT) having a first electrode coupled to first terminals of the pixel capacitor and storage capacitor. Two different common voltages are applied to a second terminal of the pixel capacitor and a second terminal of the storage capacitor, respectively. The two different common voltages are DC voltages and an absolute difference between them is based on a value in a voltage range corresponding to a transmittance range which indicates a pixel in a dark state substantially and is determined according to a minimum transmittance and a maximum transmittance of the LCD panel.