High sensitivity detection of terahertz waves can be achieved with a graphene nanomesh as grating to improve the coupling efficiency of the incident terahertz waves and using a graphene nanostructure energy gap to enhance the excitation of plasmon. Herein, the fabrication process of the FET THz detector based on the rectangular GNM (r-GNM) is designed, and the THz detector is developed, including the CVD growth and the wet-process transfer of high quality monolayer graphene films, preparation of r-GNM by electron-beam lithography and oxygen plasma etching, and the fabrication of the gate electrodes on the Si3N4 dielectric layer. The problem that the conductive metal is easy to peel off during the fabrication process of the GNM THz device is mainly discussed. The photoelectric performance of the detector was tested at room temperature. The experimental results show that the sensitivity of the detector is 2.5 A/W (@ 3 THz) at room temperature.