A light source device capable of preventing luminance from being decreased, a driving method of the light source device and a display device having the light source device are disclosed. Alight source device includes a plurality of light-emitting diode (“LED”) strings and an LED driving circuit. The LED strings include LEDs emitting lights connected in serial. The LED driving circuit supplies a driving voltage to the LED strings. The LED driving circuit maximizes the driving voltage supplied to the LED strings by using the minimum string current of string currents supplied to each LED string in an initial driving period. The LED driving circuit supplies the maximum driving voltage to the LED strings by blocking a current flowing through a sensing resistor disposed to sense the minimum string current in a normal driving period.