A method of driving an organic light emitting diode (OLED) display device that displays grayscales in a time-division manner and can prevent the occurrence of false contours and flickers at an interface between neighboring grayscales when displaying sequential images, such as moving images, at a high speed. The method is an interlaced scanning method in which a single frame is divided into an odd-numbered field and an even-numbered field that are sequentially driven, and includes dividing each of the odd-numbered field and the even-numbered field into x sub-frame groups; dividing each of a plurality of sub-frames corresponding to bits of driving data into y divided sub-frame portions; and disposing the y divided sub-frame portions in different ones of the x sub-frame groups.