To maximize reversible H-2 storage near room temperature and modest pressures, we propose Li doping of the metal-organic framework (MOFs) structures developed by the Yaghi group at UCLA (constructed using octahedral Zn-O-C clusters with aromatic carbon ring linkers). We tested this design using grand canonical Monte Carlo simulations with first-principles derived force fields and predict that at -30 degrees C and 100 bar the Li-MOF-C30 leads gravimetric H-2 uptake of 6.0 wt %, reaching the 2010 Department of Energy target (6.0 wt % in the temperature ranges of -30 to 80 degrees C and pressures <= 100 bar). Thus this promising material for practical hydrogen storage is worthy of developing experimental procedures for synthesis and characterization.