Low-temperature-grown GaAs (LT-GaAs) possesses high carrier mobility, fast charge trapping, high dark resistance, and large threshold breakdown voltage, which make LT-GaAs a fundamental material for fabricating the ultrafast photoconductive switch, high efficient terahertz emitter, and high sensitive terahertz detector. Although lots of researches have been done on the optical and optoelectrical properties of LT-GaAs, the ultrafast dynamics of the photoexcitation and the relaxation mechanism are still unclear at present, especially when the photocarrier density is close to or higher than the defect density in the LT-GaAs, the dispersion of photocarriers shows a complicated pump fluence dependence. With the development of THz science and technology, the terahertz spectroscopy has become a powerful spectroscopic method, and the advantages of this method are contact-free, highly sensitive to free carriers, and sub-picosecond time resolved. In this article, by employing optical pump and terahertz probe spectroscopy, we investigate the ultrafast carrier dynamics of photogenerated carriers in LT-GaAs. The results reveal that the LT-GaAs has an ultrafast carrier capture process in contrast with that in GaAs wafer. The photoconductivity in LT-GaAs increases linearly with pump fluence at low power, and the saturation can be reached when the pump fluence is higher than 54 J/cm2. It is also found that the fast process shows a typical relaxation time of a few ps contributed by the capture of defects in the LT-GaAs, which is strongly dependent on pump fluence: higher pump fluence shows longer relaxation time and larger carrier mobility. By employing Cole-Cole Drude model, we can reproduce the photoconductivity well. Our results reveal that photocarrier relaxation time is dominated by the carrier-carrier Coulomb interaction: under low carrier density, the carrier-carrier Coulomb interaction is too small to screen the impurity-carrier scattering, and impurity-carrier scattering plays an important role in the photocarrier relaxation process. On the other hand, under high pump fluence excitation, the carrier-carrier Coulomb interaction screens partially the impurity-carrier scattering, which leads to the reduction of impurity-carrier scattering rate. As a result, the photocarrier lifetime and mobility increase with increasing pump fluence. The experimental findings provide fundamental information for developing and designing an efficient THz emitter and detector.