The atom-bond sum-connectivity (ABS) index of a graph is a variant of several well-known chemical topological indices, such as the randi´c index, the sum-connectivity index and the atom-bond connectivity index. For a graph G = (V (G), E(G)), the ABS index of G is defined as&nbsp; <div> &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; ABS(G) = X uv∈E(G) s 1− 2 dG(u)+dG(v) , </div> <div> <span>where dG(u) denotes the degree of the vertex u in G. A cactus is a connected graph in which each block is either an edge or a cycle. For two integers n ≥ 2 and k ≥ 0, let G(n, k) be the set of cacti of order n and with k cycles. Obviously, G(n, 0) is the set of all trees of order n and G(n, 1) is the set of all unicyclic graphs of order n. We will determine the maximum ABS index of graphs among G(n, k), and also characterize the corresponding extremal graphs.</span> </div>