The rotation, translation, and vibration of many amino acid molecules fall in the terahertz (THz) range, thus qualitative and quantitative researches of amino acids can be carried out through their THz absorption characteristic fingerprint peaks. In this work, the room-temperature THz absorption spectra of DL-glutamic acid and its monohydrate at 0.5–3.0 THz are measured by utilizing terahertz time-domain spectroscopy (THz-TDS). It is found that the THz characteristic peaks of these two amino acids are obviously different from each other. Moreover, according to the changes of the absorption amplitude of the characteristic absorption peak (1.24 THz) of DL-glutamate monohydrate at different sample concentrations, the mixed samples of DL-glutamate and its monohydrate are quantitatively analyzed, and the quantitative analysis formula is verified. In addition, the optical mode of DL-glutamic acid and its monohydrate in THz region are predicted by using density functional theory (DFT). On condition that the theoretical data are matched with the experimental peaks, the origins of THz absorption peaks obtained in the experiment are discussed and summarized. The results show that the THz characteristic peaks (<2.80 THz) of DL-glutamic acid and its monohydrate come from the intermolecular interactions, and the other absorption peaks result from the combination of intermolecular and intramolecular interactions.