This paper presents a theoretical analysis of the low-frequency phonons of L-alanine by using the solid-state density functional theory at the Gamma point. We are particularly interested in the intramolecular vibrations accessing low-frequency phonons via harmonic coupling with intermolecular vibrations. A new mode-analysis method is introduced to quantify the Vibrational characteristics of such intramolecular vibrations. We find that the torsional motions Of COO- are involved in low-frequency phonons, although COO- is conventionally assumed to Undergo localized torsion. We also find the broad distributions of intramolecular vibrations relevant to important functional groups of amino adds, e.g., the COO- and NH3+ torsions, in the low-frequency phonons. The latter finding is illustrated by, the concept of frequency distribution of vibrations. These findings' may lead to immediate implications in other amino acid systems.