Using the methods based on the technique of self-similar analyzing, we find the parabolic asymptotic self-similar analytical solutions with third-order dispersion effect of constant coefficient Ginzburg-Landau equation which considers both the influence of high order dispersion and gain dispersion on the evolution of self-similar pulse. The self-similar amplitude function, phase function, strict linear chirp function and effective temporal pulse width are given in the paper. The results show that self-similar pulses still have linear chirp and remarkable third-order dispersion effect. And these theoretical results are consistent with numerical simulations.