A method and apparatus for driving an electro-luminescence display device capable of preventing a defect of signal lines caused by a relatively high scan voltage and current is disclosed. In the apparatus, a display panel has a scan line, a data line intersecting the scan line and supplied with a data, and a light-emitting device positioned at the intersection between the scan line and the data line. A data driver supplies a data to the data line. A scan driver applies a scanning pulse having a different current component to the scan line during a desired period.