Provided are a method and apparatus for driving an electro-luminescence (EL) display panel having data electrode lines and scanning electrode lines intersecting each other at a predetermined distance and EL cells, formed at the intersections thereof. In the method and apparatus, a booting current corresponding to a magnitude change of a display data signal in the next horizontal drive time period with respect to a display data signal in the current horizontal drive time period is applied to each of the data electrode lines at the beginning of the next horizontal drive time period. Instantaneous values of the booting currents are kept constant, and the application time for the booting current is proportional to a magnitude change of each display data signal in the next horizontal drive time period with respect to the display data signal in the current horizontal drive time period.