An object is to provide a rectifier circuit of which the drop in the output voltage by the threshold voltage of a transistor used as a rectifier element is suppressed. Another object is to provide a rectifier circuit whose variations in the output voltage are suppressed even in the case where the amplitude of input AC voltage varies greatly. A transistor may be used as a rectifier element in such a way that a gate electrode of the transistor is connected to a second electrode of the transistor through a capacitor, and the potential of the gate electrode is held to be higher than the potential of the second electrode by a difference greater than or equal to the threshold voltage.