Although terahertz waves are susceptible to water of crystallization (bound water), we found that the terahertz absorption spectra of cysteine hydrochloride (LCH) and its monohydrate (LCHM) are highly similar. To explain this particular phenomenon, density functional theory (DFT) and the independent gradient model (IGM) were used to obtain the vibration mode and intermolecular interaction of LCH and LCHM. The molecular polarities of LCH and LCHM were then obtained by calculating their molecular polarity index (MPI). The characteristic peak positions in the terahertz spectra of LCH and LCHM basically corresponded, with the superimposed interference of vibration modes and the van der Waals interaction between molecules concealing the expression of hydrogen bonds produced by bound water in the LCHM terahertz spectrum. In addition, the intensity of the characteristic peaks in the LCHM terahertz spectrum was higher because of its higher molecular polarity. In general, the analysis method combining THz-TDS and MPI provides a new theoretical reference for studying the relationship between biomolecules and water.