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We propose a method of measuring the terahertz (THz) Raman spectra of a material. As Raman spectroscopy is a measurement of the relative frequency spectrum relative to the frequency of the excitation source, it is not necessary to use an expensive THz source and THz detector. Instead, an ultraviolet, visible, or infrared excitation source and corresponding detector can be used. A combination of prisms and gratings is used to widen the field of view at high resolution. The resolution of the system is 4.945 cm−1 (0.149 THz), and the spectral range is 2531.84 cm−1 (75.963 THz). We measured the THz Raman spectra of solid powder, aqueous solutions, and mixtures, and studied the effects of environment, container material, and time of measurement on the spectra. The results show that the system is not significantly affected by interference from the water environment and has good stability and repeatability. This method can be applied in many fields such as material detection and environmental protection.