Non-dissociative chemisorption solid-state storage of hydrogen molecules in host materials is promising to achieve both high hydrogen capacity and uptake rate, but there is the lack of non-dissociative hydrogen storage theories that can guide the rational design of the materials. Herein, we establish generalized design principle to design such materials via the first-principles calculations, theoretical analysis and focused experimental verifications of a series of heteroatom-doped-graphene-supported Ca single-atom carbon nanomaterials as efficient non-dissociative solid-state hydrogen storage materials. An intrinsic descriptor has been proposed to correlate the inherent properties of dopants with the hydrogen storage capability of the carbon-based host materials. The generalized design principle and the intrinsic descriptor have the predictive ability to screen out the best dual-doped-graphene-supported Ca single-atom hydrogen storage materials. The dual-doped materials have much higher hydrogen storage capability than the sole-doped ones, and exceed the current best carbon-based hydrogen storage materials.