An organic EL display device for compensating for a reduction of the voltage between the gate and source of a driving transistor occurring due to a voltage drop of the source voltage caused by the resistance component of a power source line, and a method for driving the organic EL display device. The organic EL display device has a data driver for receiving digital image data and applying the digital image data and a data voltage corresponding to the position of a pixel circuit. The data driver outputs different data voltages depending on the position of the pixel circuit even when the same digital image data are received. When the driving transistor is a P-type transistor, the data driver applies a higher data voltage to a pixel circuit that is closer to an external voltage source than that applied to a farther one even when the same digital data are received. When the driving transistor is an N-type transistor, the data driver applies a lower data voltage to a pixel circuit that is closer to an external voltage source than that applied to a farther one even when the same digital data are received.