The study of topological indices - graph invariants that can be used for describing and predicting physicochemical or pharmacological properties of organic compounds - is currently one of the most active research fields in chemical graph theory. In this paper we study the Schultz index and find a relation with the Wiener index of the armchair polyhex nanotubes TUVC6[2p,q]. An exact expression for Schultz index of this molecule is also found.