Terahertz radiation generated by ultra short laser pulses has a broad band width in the far-infrared band.It is a new research field on terahertz wave interacting with materials,especially bio-materials.In this paper we studied five kinds of vegetable oil and two kinds of animal fats under different states using THz-TDS(THz time-domain spectroscopy).The refractive index and absorption coefficient of these materials are presented in the range from 0.2 to 1.6THz.The result hows that different oils have different refractive indices.The refractive indic es of vegetable oils have a gentle decline and the refractive indices of animal fats increase with temperature.The coefficients of absorption also increase with frequency.It's a meaningful result for the applications of biomedical sensing a nd imaging.