A semiconductor device including an integrator circuit, in which electric discharge from a capacitor can be reduced to shorten time required for charging the capacitor in the case where supply of power supply voltage is stopped and restarted, and a method for driving the semiconductor device are provided. One embodiment has a structure in which a transistor with small off-state current is electrically connected in series to a capacitor in an integrator circuit. Further, in one embodiment of the present invention, a transistor with small off-state current is electrically connected in series to a capacitor in an integrator circuit; the transistor is on in a period during which power supply voltage is supplied; and the transistor is off in a period during which supply of the power supply voltage is stopped.