A fin field-effect transistor (FET) and a method for forming the fin FET are provided. The method comprises: providing a semiconductor substrate in which a plurality of first grooves are formed; and forming a silicon germanium layer, fully filling the first grooves, on the semiconductor substrate; etching a certain thickness of the silicon germanium layer, forming a plurality of second grooves in the silicon germanium layer; planarizing the sidewalls of the second grooves and the silicon germanium layer at the bottom; forming an indium phosphide layer, fully filling the second grooves, in the second grooves; and back etching to remove the silicon germanium layer between the indium phosphide layers so as to expose the sidewall surface of the indium phosphide layer; forming an indium gallium arsenide layer on the top and sidewall surfaces of the indium phosphide layer; forming a high-K dielectric layer on the surface of the indium gallium arsenide layer; and forming a metal gate electrode on the high-k dielectric layer. The carrier mobility of the fin FET is improved.