There is provided a method of driving a backlight of a liquid crystal display device capable of eliminating leakage of light from adjacently-placed light emitting blocks. A gray level and maximum gray level of an input video signal are inputted for every light-emitting block. An output average gray level is calculated and a lighting control signal corresponding to converted luminance is outputted. The drivers responding to the lighting control signal makes LEDs (Light Emitting Diodes) emit light. An average gray level from an output from sensors is calculated. An average gray level, based on an average gray level and a light leakage rate, by taking light leakage into consideration. A gray level correcting signal is outputted in the light-emitting block based on the above output average gray level. An output average gray level is corrected in response to a gray level correcting signal.