Terahertz (THz) radiation, generated by ultra short laser pulses, occupies a broad band on electromagnetic spectrum chart. This radiation band belongs to far-infrared. It is a new research field of studying THz radiation interacting with materials especially with biomaterials. The paper shows experimental results of five plant oil samples from different kind of plants and two kinds of animal fat samples by using THz-TDS (THz time-domain spectroscopy) technology. The refraction indices and the absorption coefficients of these samples are measured in the range from 0.2 to 2.0 THz. The results show that different oils have different refraction indices. For oil samples, refraction indices decrease slowly while their coefficients of absorption increase with the increases of THz frequency. For the animal fat samples, the refraction indices show almost no change while the absorption coefficients increase with the increasing THz frequency. The absorption coefficients increase with the increasing temperature.