In the implementation of field effect transistor ( FET) terahertz ( THz) detectors, the integration of properly designed planar antennas could effectively enhance the coupling efficiencies betw een the transistors and THz radiation, thus improving the responsivities of THz detectors. A method to design the planar antenna w hich is based on the simulation of channel electric field at the gate edge of FET is reported here. This method is suitable for the situation w here the input impedances of FETs may not be conveniently obtained in the THz regime. The validity of this method in the antenna design is confirmed by the measurements of the fabricated Ga N/Al Ga N FET THz detectors. The maximum responsivities of the bow tie detector and the dual-dipole detector are obtained at170. 7 GHz ( 1 568. 4 V/W) and 124. 3 GHz ( 1 047. 2 V/W) respectively, w hich are close to the simulation results of channel electric field at the gate edge of the bow tie detector and the dual-dipole detector.