A semiconductor device having a field-effect transistor, including a trench in a semiconductor substrate, a first insulating film in the trench, an intrinsic polycrystalline silicon film over the first insulating film, and first conductivity type impurities in the intrinsic polycrystalline silicon film to form a first conductive film. The first conductive film is etched to form a first gate electrode in the trench. A second insulating film is also formed in the trench above the first insulating film and the first gate electrode, and a first conductivity type doped polycrystalline silicon film, having higher impurity concentration than the first gate electrode is formed over the second insulating film. The doped polycrystalline silicon film is provided in an upper part of the trench to form a second gate electrode.