In order to solve the problem of low pumping efficiency of terahertz wave due to the dispersion effect of femtosecond laser pulse transmission in optical fiber, aiming at the dispersion characteristics of femtosecond laser pulse in terahertz time-domain spectrum system, the mathematical models of angular dispersion and time-domain dispersion are established through theoretical analysis. The effects of grating pair spacing and incident angle of system optical path on dispersion compensation are numerically simulated by ray tracing method under three different grating constants. The results show that the dispersion of the system increases with the raise of grating pair spacing when the grating constant is given. When different grating constants are selected, the variation trend of dispersion is different with the change of incident angle, but the total dispersion increases with the increase of grating constant. The rationality of selecting a grating with a grating constant of 1200 mm^-1 is verified from the two aspects of spacing and incident angle. Finally, the pulse compression effect of the grating pair is proved by experiments, which meets the pulse compression requirements of terahertz time-domain spectroscopy system.