The first geometric-arithmetic index GA 1 .G/, which was introduced by D. Vukičević and B. Furtula recently, is a graph-based molecular structure descriptor. The aim of this paper is to obtain new inequalities involving the geometric-arithmetic index GA 1 and other well known topological indices. In particular, we relate the geometric-arithmetic index of a graph G with its first Zagreb index M 1 .G/, its second Zagreb index M 2 .G/, its modified Zagreb index Z 1 .G/ and its Randić index R.G/.