An organic electroluminescence display transmits a data driving voltage to a data driving unit to make different a voltage of the data signal outputted from the data driving unit, the data driving voltage being in a different level in every subframe according to the digital data signal, and displaying a desired grey level of an image by allowing a desired subframe to emit light according to the number of bits of the data signal, and a driving method thereof. An organic electroluminescence display includes a plurality of scan lines to transmit a scan signal; a plurality of data lines to transmit a digital data signal; and a plurality of pixels defined by a plurality of power supply lines to supply power, wherein the scan signal is transmitted to a plurality of subframes, and ON signals of the digital data signal have different voltages in a plurality of the subframes.