We perform density functional calculations to investigate the adsorption of molecular hydrogen on Ti-doped zigzag graphene nanoribbons using a nonlocal van der Waals functional that has recently been proposed for accurate description of exchange and correlation effects in weakly bound systems. Our results show that the adsorption of a single H-2 molecule is dissociative in purely energetic terms, but there exists an energy barrier that prevents dissociation when the molecule is deposited on the Ti-doped graphene nano-ribbon. When the Ti atom is adsorbed at a central or lateral hole site, each atom can bind up to four H-2 molecules, in each case satisfying the binding energy criterion specified by the U.S. Department of Energy for novel hydrogen-storage materials. On this basis, one can consider an effective hydrogen coverage on Ti-coated graphene nanoribbons with gravimetric density beyond the target of 6%. Copyright (C) 2015, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.