Herein, a super-resolution terahertz wave spectrometer system is proposed based on optical interference theory. The interference system can be used for the multipoint simultaneous detection of signals based on a self-developed broadband GaN array detector. The proposed spectrometer has high precision and can achieve super-resolution. The beam quality of the source to be tested can be measured based on the two-dimensional intensity distribution obtained by the proposed array detector. Continuous terahertz waves, generated by a multiplier-chain emission source with a frequency range from 470 to 720 GHz, are used as the testing source to verify the proposed spectrometer. At a detection distance of 75 mm, the spectral resolution and the measurement accuracy are determined to be 100 MHz and 0.1%, respectively. These values are 20 times the resolution and accuracy limits under the same detection conditions.