Based on the fiber link consisting of a section of a positive-dispersion and a negative-dispersion optical fiber, a method of pulse compression is proposed. The parabolic self-similar pulses are generated through a normal-dispersion fiber, then compressed by an anomalous dispersion fiber. The effect of initial chirp on pulse shaping is numerically investigated with the symmetrical distribution Fourier method. By introducing a dimensionless factor to characterize the pulse shape, it is found that, the initial negative chirp accelerates pulse shaping and the initial positive chirp is apt to broaden the range of best linear chirp of the best parabolic pulse. And the effect of third-order dispersion on pulses compression is theoretically and numerically investigated. The results show that the third-order dispersion can be weakened by using third-order dispersion partial compensation fiber.