Abstarct: One of the special applications of graph theory in chemistry is energy of graph. Since the energy of a graph is the same as total -electron energy of benzenoid structures, Therefore in this thesis has been tried to investigate the energy of these structures. For this purpose, we will define energy of graph and introduce it for benzenoid structures. But because of diversity of these systems, examination of all kinds of them is a complicated, but in this work it has been tried to investigate of each sample. These structures are divided to two clusters of c.c and p.c. So, from the first cluster we will investigate two kinds of branched and unbranch and we will represent a sequential relationship for each kind of them. From the second cluster, we will introduce only double hexagonal chains as a p.c system and as a generalization from section four; we will represent a sequential relationship for these systems. At the end, by regarding to the relationship of energy of graph, and since it is needed to calculation of eigenvalues and these calculations are very complicated and difficult for large graphs. In this collection it has been tried to reduce calculations as possible. For this case we will represent optimal methods for caculations of these values.