Using the method based on the technique of symmetry reduction, we find the general analytical parabolic asymptotic self-similar solutions for the varying coefficient of Ginzburg-Landau equation that take consideration of the influence of the doped fiber retarding time. The parabolic asymptotic amplitude function, change of strict linear phase chirp and the effective temporal pulse width of self-similar pulse with gain dispersion are given for the dispersion decreasing fibers with longitudinal exponential distribution and hyperbolic distribution. And these theoretical results have been confirmed by numerical simulation in this paper.