The present invention relates to a power supply that is adaptive for improving energy conversion efficiency and a driving method thereof and an apparatus and method for driving an electroluminescence display device using the same. A power supply that supplies a driving power to drive a driving apparatus according to an embodiment of the present invention includes a power source to supply DC power; and a DC-DC converter to convert the DC power from the power source to a level of 1/N (provided that N is a positive integer of not less than 2) times the driving power, and then to convert the converted DC power of 1/N times to a level of the driving power.