Characteristics of a semiconductor device are improved. A method of manufacturing a semiconductor device of the invention includes a step of forming a gate insulating film over a nitride semiconductor layer. The step includes steps of forming a crystalline Al2O3 film on the nitride semiconductor layer, forming a SiO2 film on the Al2O3 film, and forming an amorphous Al2O3 film on the SiO2 film. The step further includes steps of performing heat treatment on the amorphous Al2O3 to crystallize the amorphous Al2O3, thereby forming a crystalline Al2O3 film, and forming a SiO2 film on the crystalline Al2O3 film. In this way, since a film stack, which is formed by alternately stacking the crystalline Al2O3 films and the SiO2 films from a bottom side, is used as the gate insulating film, threshold voltage can be cumulatively increased.