Abstarct: Mathematics in recent decades estimates graphs energy by graph aspects and efforts detection of simple methods for graph energy. result of this efforts becomes simple method by Ivan Gutman.in this thesis therformore on Gutman method investigation ,by new methods molecule energy, estimate fuzzy energy for graph.for this purpose, concepts and definitions are presented in first chapter the definitions and concpts related to mathematics and chemistry scinces. The second chapter describes the results of the graph energy that already exists and about that discussed briefly. In third chapter by combining fuzzy math and molecule energy concepts, presents new methods that are baxsed on the properties of bonds and in fourth chapter by new methods, investigate and estimate fuzzy energy of molecule that is same structure.