Ellagic acid is a polyphenol found in many species of plants. It plays an impotent role in inhibiting proliferation and inducing apoptosis of cancer cell. The ellagic acid also has the effect of antioxidation and radioresistance. It was used in a lot of medicine and health products. Terahertz time-domain spectroscopy (THz-TDS) is a new coherent spectral technique. The spectral characteristics of ellagic acid in the range of 0.2~2.4 THz were measured by THz-TDS. The vibration absorption spectrum of the single molecule between 0.2 and 2.4 THz is simulated based on the density functional theory (DFT). It is found that the ellgic acid has the spectral response to THz radiations in this frequency region, and it shows abnormal dispersion and absorption peaks at 0.44 THz, 0.73 THz, 0.99 THz, 1.26 THz, 1.58 THz, 1.87 THz and 2.19 THz.