A method and apparatus for driving an electro-luminescence display panel capable of preventing an initial blinking phenomenon occurring at a power application is disclosed. In the method, a first electrode of the EL cell and a ground voltage source are opened during a first period from a turn-on time of a power source to shut off a current path of the EL cells. Then, the first electrode of the pixel matrix and the ground voltage source is shorted during a second period to form a current path such that the EL cells are light-emitted in accordance with a data supplied to the pixel matrix.