An organic light emitting diode display device and a driving method are provided. The organic light emitting diode display device comprises a data driver that generates a plurality of reference data voltages that have a level proportional to a gray scale level of a digital data supplied from the timing controller. The data driver supplies the data voltages to the plurality of data lines and compensates for the data voltages in accordance with a magnitude of the feedback voltages from the plurality of pixels fed back through the plurality of feedback lines under control of the timing controller.