A lamp driving apparatus includes a lamp driving power system providing a driving power to a lamp, a sensor detecting whether the lamp is turned on, and a controller controlling the lamp driving power system to provide an initial driving power to the lamp to turn on the lamp, and to provide an excess driving power to the lamp if the sensor detects that the lamp is not turned on, the excess driving power having a higher voltage level than the initial driving power. A liquid crystal display includes the lamp driving apparatus and a driving method thereof includes a lamp that is stably driven at an initial stage of operation.