Ab initio calculations show that Ca can decorate organic linkers of metal-organic framework, MOF-5, with a binding energy of 1.25 eV. The Ca-decorated MOF-5 can store molecular hydrogen (H-2) in both high gravimetric (4.6 wt %) and high volumetric (36 g/l) capacities. Even higher capacities (5.7 wt % and 45 g/l) can be obtained in a rationally designed covalent organic framework system, COF-alpha, with decorated Ca. Both density functional theory and second-order Moller-Plesset perturbation calculations show that the H-2 binding in these systems is significantly stronger than the van der Waals interactions, which is required for H-2 storage at near ambient conditions.