A method of driving a display panel in an organic light-emitting display device is provided. The method determines whether a single color image is displayed on the display panel or a multiple color image is displayed on the display panel, applies an initialization voltage, for initializing an anode of an organic light-emitting element included in a non-light-emitting pixel, to the anode of the organic light-emitting element included in the non-light-emitting pixel when the multiple color image is displayed on the display panel, and applies a lateral leakage prevention voltage that is higher than the initialization voltage to an anode of an organic light-emitting element included in an adjacent non-light-emitting pixel that is located within a reference distance from a light-emitting pixel when the single color image is displayed on the display panel.