The subject of this paper is a new idea of how to get around problems of irreversibility and low capacity of the graphene hydrogen storage. The clue is using a composite of nanoelectromechanical systems (NEMS) graphene and hydrogen for hydrogen storage. Basic scheme of attosecond nanotechnology of the reversible hydrogenation-dehydrogenation of the NEMS graphene hydrogen storage is proposed. The relaxation of the NEMS composite consisting of small graphene nanosheets and hydrogen biradicals is described by the quantum NEMS-kinetics method. As a result of computer simulation the dependence physicochemical characteristics of the NEMS composite on concentration of hydrogen, size of graphene nanosheets, temperature and time of relaxation is revealed. The theoretical substantiation that the NEMS composite stands as promising candidate to easily reversible and highly capacious hydrogen storage is given.