Let G=(V, E) be a simple connected graph. The sets of vertices and edges of G are denoted by V= V (G) and E= E (G), respectively. In such a simple molecular graph, vertices represent atoms and edges represent bonds. In chemical graph theory, we have many topological indices for a molecular graph. The First and Second Zagreb indices are equal to M1 (G)=∑ uv∈ E (G)[du+ dv] and M2 (G)=∑ uv∈ E (G) dudv, respectively. In this paper, we focus on the structure of Capra-designed planar benzenoid series Cak (C6)(k≥ 0), and compute its Generalized Zagreb index.