Ultrashort pulses can evolve into self-similar parabolic pulses with a linear chirp in optical fiber amplifiers with normal group velocity dispersion, and the evolution result can affect the consequent pulse compression. The influences of the initial pulse width and energy as well as fiber dispersion and gain coefficient on the pulse self-similar evolution were numerically studied by split-step Fourier method, and the results reveal that dispersion length is the key factor determining whether the pulse can evolve self-similarly or not. When the dispersion length is close to fiber length (just severalfold), the initial pulse can evolve into a parabolic pulse; the larger the difference between the dispersion length and fiber length, the worse the self-similar evolution. Increasing the initial pulse energy can accelerate the pulse self-similar evolution, and therefore decrease the distance for self-similar evolution. Under a given amplifier total gain the higher the gain coefficient is, for the effect of nonlinear distortion, the worse the self-similar evolution is. When the gain coefficient is 0.95 m-1, the total gain of the amplifier is 3.3 dB larger than that when the gain coefficient is 3.8 m-1.