A method and apparatus for driving an ElectroPhoretic Display (EPD) are provided, in which upon sensing a request for displaying data in a gradual graphic representation scheme, a plurality of segments for displaying the data are determined, a display changing order of the segments is determined, an inter-segment time interval is calculated, driving voltage pulses are applied to a first segment according to the display changing order, and driving voltage pulses are applied to each of the other segments at the inter-segment time interval after driving voltage pulses are applied to a previous segment according to the display changing order.