Food additives butyl hydroxy anisole (BHA) and its mixtures with polythene of different ratio are measured by using terahertz time domain spectroscopy (THz-TDS) technology, and the absorption spectrum and refractive index spectrum of 0.2～2.6 THz band are obtained. Experimental results show that there are three obvious absorption peaks of the sample in the band, which locates at 0.64, 1.14, 1.81 THz, respectively. The fingerprint spectrum can be used for the detection and identification of the substance in THz band. The terahertz spectra of BHA mixture are analyzed by the least squares method. Results show that the correlation coefficient between the terahertz absorption coefficient and mass fraction of BHA is larger than 0.98. The numerical calculation of single-molecule BHA is carried out with density functional theory. It is indicated that the terahertz absorption peaks have relationship with molecular conformation and molecular internal motion.