A continuous 4–32 THz emission spectrum of organic crystal DAST is obtained through a widely tunable quasi-monochromatic terahertz source and sensitive up-conversion detection. The spectrum is characterized by a frequency resolution of ∼0.05 THz and a highest signal-to-noise ratio of ∼65 dB. Terahertz signals are detectable at room temperature even in the high absorption regions of DAST, thus most of the absorption peaks of DAST are clearly located. The results verify the findings of previous works well, including density functional theory calculations and other similar experiments. This paper provides a highly sensitive instrument for broadband terahertz spectroscopic characterization.