Fiber amplifier is used to compensate for the transmission loss of optical signals in the fiber. It is key device in all-optical communication network. The physical model for propagation of optical soliton in the distributed fiber amplifier is established. The properties of propagation and amplification for optical soliton were simulated numerically using split-step Fourier transform method. The influence of gain dispersion on the profile and power spectrum of optical soliton was discussed finally. The results show that the chirped soliton is produced continuously with the amplification of optical soliton in the anomalous dispersion regime of amplifier. The power spectrum of soliton is widened and the oscillation structure is produced. The gain dispersion of amplification medium leads to optical soliton amplitude decreasing, width broadening and power spectrum narrowing. So the dispersion, nonlinear effect and gain dispersion of fiber amplifier all have influences on the propagation property of optical soliton.