A Light Emitting Diode (LED) driving apparatus and a method of driving a LED backlight unit are provided. An LED driving apparatus includes: an input unit configured to receive a dimming signal, an extension unit configured to extend ON time of the inputted dimming signal, an LED driving unit configured to drive an LED array using the extended dimming signal, and a detection unit configured to detect a degradation of the LED array by measuring a forward voltage between the LED array and the LED driving unit.