As a typical 2D coating material, graphene has been utilized to effectively reduce secondary electron emission from the surface. Nevertheless, the microscopic mechanism and the dominant factor of secondary electron emission suppression remain controversial. Since traditional models rely on experimental bulk properties data which is scarcely appropriate for the 2D coating situation, this paper presents a first-principles based numerical calculation of the electron interaction and emission process for monolayer and multilayer graphene on the silicon (111) substrate. By using the anisotropic energy loss for the coating graphene, the electron transport process can be described more realistically. The real physical electron interactions, including the elastic scattering of electron-nucleus, inelastic scattering of the electron-extranuclear electron and electron-phonon effect, are considered and calculated based on the Monte Carlo method. To be independent of experimental data, the energy level transition theory based first-principles method and the full Penn Algorithm are used to calculate the energy loss function during the inelastic scattering. Variations of the energy loss function and interface electron density difference for 1L to 4L layer graphene coating GoSi are calculated, and their inner electron distributions and secondary electron emission are analyzed. Simulation results demonstrate that the dominant factor of the SEY inhibition for GoSi is the mechanism by inducing electrons deeper during the internal scattering process. In contrast, a low surface potential barrier due to the positive deviation of electron density difference in monolayer GoSi interface inversely weakens the suppression of graphene layer on secondary electron emission. Only when the graphene layer number is 3L, the contribution of surface work function to the secondary electron emission suppression presents to be slightly positive.