The approximation of the phase introduced by self-phase modulation (SPM) is reasonably calculated and the spectrum broadening factor is given basing on nonlinear Schrdinger equation. The spectrum of propagating pulses is broadened seriously by SPM in the fiber with normal group velocity dispersion (GVD) when gain (G) exists. And the spectra broadening of the central part of pulses is quite different from that of the wings of the pulses. The self-similar evolution of Gaussian pulses is described. The temporal shape of the wings of the pulses being covered by the central part gradually is discovered. A theoretical explanation of self-similar pulses propagation is given which verified by the numerical simulation for the self-similar evolution of three kinds of pulses.