A Michelson interferometer was constructed to measure the spectra generated by a terahertz (THz) gas laser pumped by a CO2 laser. The hyperfine spectra at 2.52 THz and 3.11 THz generated in CH3OH gas pumped by the 9P36 and 9R10 laser lines of the CO2 laser was measured with the frequency resolution of around 1 GHz. The measurement results showed that the THz laser was monochromatic and had very narrow linewidth. The measured wavelength was consistent with the nominal value. Velocity measurement of target on the translation mirror was also performed based on this interferometer. Two methods for acquiring velocity were proposed, demonstrating good accordance with the set values for both fixed and variable velocities. It is concluded that the Michelson interferometer could be used to accurately measure the spectrum of a THz source, and the velocity measurement was also possible with the help of a monochromatic THz source, laying the basis for THz applications like spectroscopy, imaging, etc.