In order to study the compression characteristics of the self-similar pulse in the Mach-Zehnder interferometer(MZI), the evolution and compression of the self-similar pulse were simulated by using the nonlinear Schrdinger equation. The influence of the fiber parameters on pulse compression of the MZI based on the cascade single-mode fiber was analyzed. The results show that without considering the high-order dispersion, when the length of the two single-mode fibers in the upper arm is 8.16 m and 2.16 m, respectively, and the length of the single-mode fiber in the lower arm is 8.16 m, the optimal compression pulse is obtained with the full width at half maximum of 27.85 fs, peak power of 1860.59 W and the pedestal energy ratio is 10.241%. When high-order dispersion is considered, it is found that pulse transmission in single-mode fiber presents the phenomenon of the peak power increase and the pedestal energy ratio increase, and the right shift of pulse is not favorable to output compression pulse with a small pedestal. When the third-order dispersion is less than 0.001 ps3/km, femtosecond pulses of good quality can be obtained by using MZI compression. The result of this study has certain reference values for self-similar pulse compression research.