A method for making a field effect transistor includes providing a graphene nanoribbon composite structure. The graphene nanoribbon composite structure includes a substrate and a plurality of graphene nanoribbons spaced apart from each other. The plurality of graphene nanoribbons are located on the substrate and extend substantially along a same direction, and each of the plurality of graphene nanoribbons includes a first end and a second end opposite to the first end. A source electrode is formed on the first end, and a drain electrode is formed on the second end. The source electrode and the drain electrode are electrically connected to the plurality of graphene nanoribbons. An insulating layer is formed on the plurality of graphene nanoribbons, and the plurality of graphene nanoribbons are between the insulating layer and the substrate. A gate is formed on a surface of the insulating layer away from the substrate.