A field effect transistor includes a substrate and a semiconductor layer provided on the substrate, wherein the semiconductor layer includes a lower barrier layer provided on the substrate, Ga-face grown, lattice relaxed, and having a composition In1−zAlzN (0≦z≦1), a channel layer having a composition of: AlxGa1−xN (0≦x≦1) or InyGa1−yN (0≦y≦1). Or GaN provided on and lattice-matched to the lower barrier layer, a source electrode and a drain electrode having ohmic contact to an upper part of the semiconductor layers, disposed spaced to each other, and a gate electrode arranged via a gate insulating film in a region lying between the source electrode and the drain electrode.