To improve the characterization of the polycrystalline HMX spectroscopy, the terahertz spectrum experiment and analysis study of α-HMX were carried out using a terahertz time-domain spectroscopy. The terahertz absorption spectrum and characteristic absorption peaks of α-HMX were obtained. Based on a variety of function model of density functional theory, the calculation work of the molecular vibration frequency of α-HMX was performed. The consistency of calculated result under the various function models with the experimental data was compared. Results show that the 0.82 THz absorption frequency of α-HMX crystal is formed by the symmetrical swing of a pair of nitro groups. The 1.51 THz absorption frequency is formed by the symmetrical swing of another pair of nitro groups. The formation of 1.93 THz absorption frequency is derived from the swing and twisting of nitro groups, and a twisting of the C—H group etc. behaviors