In order to fit the total reaction cross section of exotic nuclei, by using Glauber model, we consider that the exotic nuclei is composed of a core and valence nucleon(s), the finite range correction has been added to the Glauber model, and a Fermi-density-distribution with two parameters has been chosen as the input density distribution of the core of the exotic nucleus for the special distribution of the valence nucleon(s), has a large dispersion. The results of the theoretical calculation are in agreement with the experimental one for nucleus with exotic structure, both at high and intermediate energy regions.