In this study, we investigated the pre-equilibrium effect by using a new evaluated geometry-dependent hybrid model and a neutron skin effect with density dependence for the (204,206,207)Pb(p, xn) reaction at 25.5MeV incident proton energy. We calculated the initial exciton numbers obtained from the modified Skyrme force based on fitting the fission barriers of heavy deformed nuclei (SKM*) and SLy4 for proton induced reaction on target nuclei (204,206,207)Pb. We calculated, by using a new calculation method, the initial neutron and proton exciton numbers for (204,206,207)Pb from the neutron and proton density and we investigated the shell effect by using an effective nucleon-nucleon interaction with Skyrme force. We also compared the geometry-dependent hybrid model (GDH), newly evaluated with the initial exciton number calculations of the neutron emission spectra of the (204,206,207)Pb(p, xn) reaction, with the values reported in the literature at 25.5MeV incident proton energy. The obtained results were investigated and compared with the pre-equilibrium calculations and experimental results.