The self-similar solutions of the nonlinear Schrdinger equation for the high-power pulses propagated and amplified in the gain fiber are analyzed,which result showing that when the pulse duration and energy satisfied the certain relation,the seed pulse can be propagated and amplified in the gain fiber by optimizing the length of the gain fiber.The key self-similar evolution parameters of the seed pulse in the gain fiber are investigated.When the injection energy is 400 pJ and the pulse duration is 200 fs,the propagation and amplification characteristics of the secant,Gaussian,and super Gaussian seed pulses propagated and amplified in the large mode area gain fiber whose core diameter is 30 μm are numerical simulated.The results show that the temporal and spectral profiles of the three kinds of seed pulses are evolved into parabolic profiles and broadened.However,there are strong oscillations structure on the edges of the spectral profile.Moreover,the output pulse is linearly chirped parabolic pulse,which is easy to compress and has very important significance for realizing the all fiber high power ultra-short pulse generation system.