Based on nonlinear Schrodinger (NLS) equation, self-similar region in which pulses can propagate with a parabolic intensity profile in dispersion-decreasing fiber (DDF) is established by split-step Fourier method and waveform analysis, influences of initial pulse and fiber parameters on self-similar region and the speed of evolution are also investigated. Results show that reduction of initial pulse energy can expand self-similar region but slow down the self-similar evolution. Initial pulse width has an optimum value with the widest self-similar region and relatively high evolution speed. Input pulses with Gaussian profile have a faster evolution speed and a wider self-similar region than those with hyperbolic secant profile. To get an extensive region for self-similar propagation, a DDF with smaller nonlinearity parameter can be used, and the increase of nonlinearity parameter can speed up self-similar evolution. In addition, group-velocity dispersion parameter and gain coefficient should be set at its optimum value to get the largest self-similar region and the fastest evolution speed.