Terahertz spectroscopy, as the main method to obtain the information of substances in terahertz frequency band, has been widely used in the determination of substance composition, and it has a broader application prospect in the imaging of composition distribution, such as the detection of effective components of tablets and drugs, the detection of dangerous goods in baggage security inspection and so on. The current terahertz spectral detection methods, time-domain spectroscopy (THz-TDS) and frequency-domain spectroscopy (THz-FDS), can’t take account of both spectral resolution and scanning time well, and it often takes several seconds or even minutes (depending on the structure of the spectrometer) to obtain spectral data, which makes the multi-pixel imaging system appear to be overdone. The application of terahertz spectroscopic imaging is seriously restricted because of the delay and the inability to meet the speed requirement of video imaging. At present, terahertz imaging is mostly full-band intensity imaging, which can only reflect the spatial distribution information of the sample, but can’t reflect the spectral information of the sample. Therefore, it is very urgent to improve the detection rate of terahertz spectroscopy. The realization of high-speed detection can not only greatly reduce the time-consuming of spectroscopy experiment, but also provide the possibility to realize the terahertz spectroscopic composition distribution imaging. In this paper, a high-speed detection method of terahertz spectrum based on Michelson interferometer is proposed. On the basis of designing the structure of the device, the working process is analyzed theoretically, and the terahertz spectrum is calculated. Then, the aspects of data sampling, data processing and parameter selection are analyzed, and the results show that the method can significantly speed up the acquisition rate of THz spectra. Finally, the method is modeled and simulated, and the whole detection process is simulated. Taking the spectrum distribution of terahertz radiator as an example, the simulation results of this method are compared with the test results of time domain spectroscopy (THz-TDS). It is found that the spectrum curve measured by time domain spectroscopy (THz-TDS) can be approximately regarded as the envelope of the spectrum curve obtained by this high-speed spectral detection method. The results have strong consistency. This shows that the proposed method can detect the terahertz spectra of samples, and it can significantly accelerate the spectral formation rate compared with the time-domain spectroscopy (THz-TDS) on the premise of the same resolution. It provides a possibility for practical and high-throughput terahertz spectroscopy imaging.