In this paper, we use applied mathematical modelling to investigate the storage of hydrogen molecules inside graphene-oxide frameworks, which comprise two parallel graphenes rigidly separated by perpendicular ligands. Hydrogen uptake is calculated for graphene-oxide frameworks using the continuous approximation and an equation of state for both the bulk and adsorption gas phases. We first validate our approach by obtaining results for two parallel graphene sheets. This result agrees well with an existing theoretical result, namely 1.85 wt% from our calculations, and 2 wt% arising from an ab initio and grand canonical Monte Carlo calculation. This provides confidence to the determination of the hydrogen uptake for the four graphene-oxide frameworks, GOF-120, GOF-66, GOF-28 and GOF-6, and we obtain 1.68, 2, 6.33 and 0 wt%, respectively. The high value obtained for GOF-28 may be partly explained by the fact that the benzenediboronic acid pillars between graphene sheets not only provide mechanical support and porous spaces for the molecular structure but also provide the higher binding energy to enhance the hydrogen storage inside graphene-oxide frameworks. For the other three structures, this binding energy is not as large in comparison to that of GOF-28 and this effect diminishes as the ligand density decreases. In the absence of conflicting data, the present work indicates GOF-28 as a likely contender for practical hydrogen storage.