A light source driving apparatus for sequentially driving a plurality or light sources is provided. The light source driving apparatus includes a light source power supply for supplying a power source necessary for driving the plurality of light sources, a light source controller for generating a control signal to sequentially turn on and off the plurality of light sources, a soft starter connected between the light source power supply and the light sources, for delaying the power source generated from the light source power supply for a first determined time and supplying the delayed power source to the light sources, and a control signal delayer connected between the light source controller and the light sources, for delaying an ON signal of the control signal generated from the light source controller for a second predetermined time and supplying the delayed signal to the light sources.