The self-similar evolution of an initial Gaussian pulse propagating in a nonlinearity increasing fiber (NIF) with an exponential nonlinearity profile is studied theoretically and numerically. As well as the dispersion decreasing fiber with normal group velocity dispersion (ND-DDF with a hyperbolic dispersion profile), the NIF is also equivalent to a fiber amplifier, which can generate a parabolic self-similar pulse with strictly linear chirp. Furthermore, the impacts of two equivalent ways of ND-DDF and NIF on characteristics of the self-similar evolution are studied. The theoretical and simulation results show that: 1) the equivalent gain determines the results of self-similar evolution while the equivalent method determines the process speed; 2) with the same equivalent gain, the initial pulses in ND-DDF and NIF both evolve into the same parabolic self-similar pulse, but the process of NIF is more efficient, needing a shorter fiber length; 3) the relationship of fiber lengths of NIF and ND-DDF is to make the two fibers have the same “effective amplification”.