Terahertz (THz) absorption spectra of the similarly structured molecules with amide groups including benzamide, acrylamide, caprolactam, salicylamide, and sulfanilamide in the solid phase at room temperature and 7.8 K for salicylamide are reported and compared to infrared vibrational spectral calculations using density functional theory. The results of THz absorption spectra show that the molecules have characteristic bands in the region of 0.2–2.6 THz (~7–87 cm−1). THz technique can be used to distinguish different molecules with amide groups. In the THz region benzamide has three bands at 0.83, 1.63, and 1.73 THz; the bands are located at 1.44 and 2.00 THz for acrylamide; the bands at 1.24, 1.66 and 2.12 THz are observed for caprolactam. The absorption bands are located at 1.44, 1.63, and 2.39 THz at room temperature, and at 1.22, 1.46, 1.66, and 2.41 THz at low temperature for salicylamide. The bands at 1.63, 1.78, 2.00, and 2.20 THz appear for sulfanilamide. These bands in the THz region may be related to torsion, rocking, wagging, and other modes of different groups in the molecules.