Terahertz (THz) spectroscopy provides multifaceted capabilities for observing low-energy responses of macromolecules, cells and tissues, understanding THz biophysical effects, and expecting to realize the application of THz technology in biomedicine. However, its high-frequency characteristics of limited penetration depth and strong absorption of water in the body comparable to microwaves are impeding the proliferation of THz spectroscopy. Here we show that THz spectroscopy makes possible the observation of THz anisotropy phenomena for the first time in fascia and lean tissue. Through optical microscopy, we infer that the microscopic mechanism of THz anisotropy comes from the periodic stripe structure of the biological tissue. The above related experimental findings may be expected to promote the application of THz technology in biomedicine.