Let \(MG(i,n)\) be a connected molecular graph without multiple edges on \(n\)vertices whose minimum degree of vertices is \(i\), where \(i \leq i \leq 4\). One of the newest topological indices is the first Geometric-Arithmetic index. In this paper, we determine the graph with the minimum and the maximum value of the first Geometric-Arithmetic index in the family of graphs \(M{G}(i,n)\),\(l\leq i \leq 3\).