This invention relates to a method for driving an electro-luminescence display device. The method includes the steps of selecting a scan line by applying a scan signal to any one of a plurality of scan lines; and switching between a constant voltage and a constant current to apply data to a plurality of data lines crossing the scan lines. The method switches between the constant voltage source and the constant current source to drive the data lines. As a result, it increases the brightness uniformity and brightness. Therefore, the picture quality can be sustained at a high level.