An organic light emitting display and a driving method thereof capable of reducing power consumption. A driving transistor controls a current through an organic light emitting diode of the display. A voltage controller supplies a first voltage to the anode of the OLED of at least one specific pixel and controls the cathode voltage of the OLED in correspondence to a second current through the OLED, such that the cathode voltage corresponds to the first voltage supplied to the OLED. Thus, the driving transistor can be driven in saturation mode with consistent current in spite of process variations, with a reduced power consumption.