The tight-binding electron model is the key point in the teaching of band theory in solid state physics, while the band structure analysis of tight-binding electrons in face-centered cubic lattice is a teaching difficulty. In this article, a graphical method is proposed for analyzing the energy spectrum characteristics of tightly bound electrons in a face centered cubic lattice through numerical fitting. The results show that the energy spectrum varies in different directions and the energy band bottom is located in the center of simple Brillouin zone. The two high-energy extreme points are located at the four-face center and six-face center of the reduced Brillouin zone, respectively. The band widths along simple Brillouin zone center to four-faceted and six-faceted face-centered axes are 16-fold and 12-fold overlap integral, respectively. The relevant research results can not only provide an effective method for the analysis of crystal band structure, but also provide important theoretical guidance for the teaching of solid-state physics.