Disclosed are an apparatus and method for driving an organic light emitting display device. The driving apparatus includes a display panel, a data converter, a timing controller, and a panel driver. The data converter gamma-corrects three-color input data having red, green, and blue, performs color coordinate conversion based on the gamma-corrected blue data to generate three-color conversion data and a color gamut determination signal, inversely gamma-corrects the three-color conversion data, and generates four-color image data to be supplied to a unit pixel according to the color gamut determination signal on the basis of the three-color input data and the inversely gamma-corrected three-color conversion data.