An object is to provide a convenient display device which consumes sufficiently small amount of power and a method for driving such a display device. The display device can be in an off state with a still image displayed in a still image display mode in which a pixel electrode and a common electrode which are for applying a voltage to the display element are brought into a floating state so that a voltage applied to the display element is held, and a still image is displayed without further supply of a potential. The display device is put to an off state with a desired image displayed in the still image display mode, whereby the display device can have a higher level of security and can be more convenient.