In a semiconductor device including a transistor including a gate electrode formed 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, a first oxide insulating film covering the transistor, and a second oxide insulating film formed over the first oxide insulating film, the multilayer film includes an oxide semiconductor film and an oxide film containing In or Ga, the oxide semiconductor film has an amorphous structure or a microcrystalline structure, the first oxide insulating film is an oxide insulating film through which oxygen is permeated, and the second oxide insulating film is an oxide insulating film containing more oxygen than that in the stoichiometric composition.