Based on the nonlinear Schr?dinger equation, pulse propagation in fiber and the linearly chirped parabolic pulse generation by the dispersion decreasing fiber with a normal dispersion (ND-DDF) with a hyperbolic profile, a novel scheme for the generation of the self-similar parabolic pulse by use of a comb-like profiled fiber (CDPF) with normal group-velocity dispersion is proposed. The corresponding numerical model is also presented. In this model, evolution of the self-similar parabolic pulse in the CDPF close to dispersion profile of the DDF is analyzed numerically. The results show that when the hyperbolic-secant-like pulses at 1550 nm have different initial energy and pulse width, the pulse in the CDPF can evolve into a linearly chirped pulse with an exact parabolic intensity profile.