It is not pa rticular expatiate to conformation the Fermi surface in popular solid physicsteaching material. The neighbo ring elect rons of Fermi surface inf luence the metallic character verymuch. It is very important to understand the conception of Fermi surface and the distance from Fermisurface to boundary of Brillouin zone. The constructive method of the Fermi surface of two-dimensionalsquare lattice free electron gas and the relatio nship between the Fermi surface and Brillouin zone areint roduced systematically.