The present invention relates to an organic electro-luminescence display device and a method of driving the same that is adaptive for reducing power consumption by removing an unnecessary current as well as for improving a uniformity of a display screen. An organic electro-luminescence display device according to an embodiment of the present invention includes: a display panel in which a plurality of data lines and a plurality of scan lines cross each other and electro-luminescence elements are arranged at the crosses; a pre-charge driver, which detects a gray level of digital video data to be realized at a Nth when a data current corresponding to a gray level of digital video data to be realized at a (N-1)th and calculates a pre-charge current corresponding to the detected gray level of digital video data to supply the calculated pre-charge current to the electro-luminescence elements; a data driver for supplying data to the electro-luminescence elements charged with the pre-charge current; and a scan driver for supplying a san pulse, synchronized with the data, to the scan lines.