A method of producing a semiconductor transistor involving formation of an ohmic electrode on an active layer composed of a GaN-based semiconductor includes a process of forming a first layer 11 composed of tantalum nitride on an active layer 3 and a second layer 12 composed of Al layered on the first layer 11 and a process of forming ohmic electrodes 9s and 9d in ohmic contact with the active layer 3 by heat treating the first layer 11 and the second layer 12 at a temperature of from 520° C. to 600° C.