Low-frequency modes of l-Asp and l-Asn were studied in the range from 0.1 to 3.0 THz using time-domain Terahertz spectroscopy and density functional theory calculation. The results show that PBE-D2 shows more success than BLYP-D2 in prediction of THz absorption spectra. To compare their low-frequency modes, we adopted "vibrational character ID strips" proposed by Schmuttenmaer and coworkers [Journal of Physical Chemistry B, 117, 10444(2013)]. We found that the most intense THz absorption peaks of two compounds both involve severe distortion of their hydrogen bonding networks. Due to less rigid hydrogen bonding network in l-Asp, the side chain (carboxyl group) of l-Asp exhibits larger motions than that (carboxamide group) of l-Asn in low-frequency modes.