Let G = (V,E), V = {1,2 … n}, be a simple connected graph with n vertices and m edges and let d1 ≥ d2 … ≥ dn > 0, be the sequence of vertex degrees. With i ~ j we denote the adjacency of the vertices i and j in graph G. With AG = Σi~j di+dj 2 p didj we denote arithmetic-geometric topological index. In this paper we give some new upper bounds for this topological index.