Nonlinear Schrdinger Equation is a basic equation for investigating the propagation of optical pulses in fibers. By using the split-step Fourier method, self-similar propagation of linearly chirped pulses in fibers with longitudinal gain profile is studied. It is found that, because the self-phase modulation and group velocity dispersion respectively play the main roles at different propagation distances when the signs of the group velocity dispersion coefficient and the chirp coefficient are the same, no matter what the shapes of the input pulses are, the pulses will be compressed during propagation, and with the further increasing of the propagation distance, the compressed pulses will be broadened again. The intensity distributions of the Hermite-Gaussain input pulse as well as the sine input pulse are symmetric, while that of the Laguerre-Gaussian input pulses deflect during propagation obviously because of energy exchange. When the signs of the group velocity dispersion coefficient and the chirp coefficient are different, group velocity dispersion plays the main role, and the pulse is always broadened during propagation. The results may provide a new theoretical foundation and a new method for the fabrication of pulse compressors, amplifers and the development of a new source for THz modulated beams.