A driving apparatus for an organic electro-luminescence display device for reducing a deterioration of organic light-emitting diode device in the organic electro-luminescence display device is disclosed. In the driving apparatus, a data supplier supplies a data signal to an anode of an organic light-emitting diode device. A first voltage source generates a first voltage. A second voltage source generates a second voltage higher than said first voltage. A voltage stabilizer stabilizes said second voltage to be supplied to the cathode of the organic light-emitting diode device. First and second switching devices selectively apply said first and second voltages to a cathode of the organic light-emitting diode device.