As the building blocks of proteins, amino acids serve vital metabolic functions in addition to protein synthesis and thus attract enormous interest. Here we reported the far-infrared optical properties of L-cysteine (Lcys) and its hydrochloride monohydrate (LCHM) characterized by terahertz time-domain spectroscopy. The Lcys and LCHM exhibit quite distinct characteristics in the terahertz region due to diverse collective vibrations of the molecules, which is further confirmed by the solid-state density functional theory (DFT) calculations. The presented studies indicate that the intermolecular hydrogen bonds play a critical role in the far-infrared terahertz response of Lcys and LCHM.