The quasi-two-dimensional van der Waals intrinsic ferromagnetic semiconductor CrGeTe₃ possesses both a narrow semiconductor band gap and ferromagnetic properties, which makes it have a broad application prospect in the fields of spintronics and optoelectronics. In recent years, CrGeTe₃ has received extensive attention from researchers. To the best of our knowledge, so far, these studies have mainly focused on the optical response in near infrared and visible light range, but little has been done in THz frequency range. Therefore, it is upmost importance to obtain the complex dielectric constant as well as the photocarrier dynamics of the CrGeTe₃ at the THz frequency. Herewith, we use time-domain THz spectroscopy and time-resolved THz spectroscopy to investigate the fundamental properties of the CrGeTe₃ crystal in the THz range, including refractive index and absorption coefficient in THz frequency, as well as the THz photocarrier dynamics under 780-nm optical excitation. The fundamental characterizations are carried out on a 33-μm-thick CrGeTe₃ wafer by Fourier infrared spectroscopy, X-ray diffraction and Raman scattering. It is concluded that the CrGeTe₃ wafer shows an indirect band gap of 0.38 eV and good crystalline quality. The THz time domain spectroscopy presents that the CrGeTe₃ wafer has a refractive index and an absorption coefficient of 3.2 and 380 cm^–1, respectively, both of which show almost negligible dispersion in the investigated THz frequency. Under the optical excitation of 780 nm, the subsequent photocarrier relaxation can be well reproduced by a double exponential function: the fast relaxation shows a lifetime of 1–2 ps, depending on pump fluence, which is contributed by electron-phonon coupling; the slow relaxation has a typical lifetime of 7–8 ps, which is due to phonon-assisted electron-phonon recombination. The Pump fluence and delay time dependence of THz photoconductivity dispersion can be well fitted with Drude-Smith model, and the fitted results demonstrate that the plasma frequency increases with pump fluence in a fixed delay time, and then decreases with delay time increasing at a fixed pump fluence. The momentum scattering time shows that it decreases with pump fluence increasing, and increases with delay time increasing. These pump fluence and delay time dependent fitting microscopic parameters show similar tendencies to those of a conventional semiconductor. In a word, the experimental study here demonstrates that the narrow band-gap CrGeTe₃ wafer is well transparent and disperionless in a THz frequency range. From the above bandgap photoexcitation it follows that the wafer shows fast response and high modulation depth in THz radiation, providing a useful reference for the application of CrGeTe₃ in optoelectronics and related fields.