A lamp driving apparatus of a liquid crystal display includes a plurality of lamps arranged with a predetermined distance between adjacent lamps; a comparator to compare output voltages of lamps that are separated by more than the lamp distance; and a power interceptor to cut off the power supply of a lamp where mis-discharge is generated, in accordance with a comparison result of the comparator. A lamp driving method of a liquid crystal display which includes: comparing a designated reference voltage with lamp output voltages, and intercepting the power supply of the lamp of which the output voltage is different from the reference voltage to stop mis-discharge between lamps.