Under the condition of combined effects of group-velocity dispersion and self phase modulation, the step Fourier method is used to simulate the propagation of initial chirped super Gaussian pulses inside fiber. The initial chirp influences the shapes of super Gaussian pulses in propagation process, and positive and negative chirps have different effects. For the existing of initial chirp, the splits of pulses and the spreading speed move ahead and increase. When the amplitude of super Gaussian pulses increases by 1.4 times, in the range of | C |<1.5, pulses can keep good shapes along their propagation distance. Even if | C | increases to 3.5, their shapes are also good. Most energy of pulse is still at the middle parts. These results show that, for the initial chirped super Gaussian pulses, the influence of initial chirp will be decreased by increasing the intensity of pulses. This will be of benefit to optical communication. Under the condition of combined effects of group-velocity dispersion and self phase modulation, the step Fourier method is used to simulate the propagation of initial chirped super Gaussian pulses inside fiber. The initial chirp influences the shapes of super Gaussian pulses in propagation process, and For the existing of initial chirp, the splits of pulses and the spreading speed move ahead and increase. When the amplitude of super Gaussian pulses increases by 1.4 times, in the range of | C | <1.5, Even if | C | increases to 3.5, Their shapes are also good. Most energy of pulse is still at the middle parts. These results show that, for the initial chirped super Gaussian pulses, the influence of initial chirp will be decreased by increasing the intensity of pulses. This will be of benefit to optical communication.