In the implementation of field effect transistor (FET) terahertz (THz) detectors, the integration of properly designed planar antennas could effectively enhance the coupling efficiencies between the transistors and THz radiation, thus improving the responsivities of THz detectors. A method to design the planar antenna which 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 where 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 GaN/AlGaN FET THz detectors. The maximum responsivities of the bowtie detector and the dual-dipole detector are obtained at 170 7 GHz (1568.4 V/W) and 124.3 GHz (1047.2 V/W) respectively, which are close to the simulation results of channel electric field at the gate edge of the bowtie detector and the dual-dipole detector.