AbstractLet G be an undirected and simple graph on n vertices. Let ω, α and χ denote the number of components, the independence number and the connectivity number of G. G is called a 1‐tough graph if ω(G – S) ⩽ |S| for any subset S of V(G) such that ω(G − S) > 1. Letσ2 = min {d(v) + d(w)|v and w are nonadjacent}.Note that the difference α ‐ χ in 1‐tough graph may be made arbitrary large. In this paper we prove that any 1‐tough graph with σ2 > n + χ ‐ α is hamiltonian.