A semiconductor device includes a transistor including a gate electrode over a substrate, a gate insulating film covering the gate electrode, a multilayer film overlapping with the gate electrode with the gate insulating film provided therebetween, and a pair of electrodes in contact with the multilayer film, and an oxide insulating film covering the transistor. The multilayer film includes an oxide semiconductor film and an oxide film containing In or Ga, the oxide insulating film contains more oxygen than that in the stoichiometric composition, and in the transistor, by a bias-temperature stress test, threshold voltage does not change or the amount of the change in a positive direction or a negative direction is less than or equal to 1.0 V, preferably less than or equal to 0.5 V.