Metal-organic frameworks (MOFs) have emerged as extended-network, highly tunable, crystalline hydrogen storage adsorbents. The uptake of H2 on Zn4O-based MOFs with different linkers was studied in the current work. The binding energies, consecutive binding energy and step energy of H2 adsorption on MOF-177, MOF-200 and a newly defined MOF (named NEW-MOF) have been calculated on different possible sorption sites, using DFT/Dmol3 /PBE. The linkers have the same benzene ring in center, but different numbers of phenyl rings, including 3, 6 and 9 phenyl rings in MOF-177, MOF-200 and NEW-MOF around the center ring, respectively. Our study results showed that the binding energy of the H2 molecules with the linker NEW-MOF was -4.165 kcal/mol, more negative than those obtained for MOF-177 (-3.276 kcal/mol) and MOF200 (-3.438 kcal/mol). The obtained thermo-favorability may be attributed to the less steric hindrance for adsorption of H2 on the MOF with the larger linker. Step energy results showed that the linkers of MOF-177, MOF-200 and NEW-MOF could adsorb 7, 9 and 12 number of H2 molecules, respectively. Results also disclosed adsorbed moles of H2 per 1×1×1 unit cell of the MOFs decreases with increasing the linker length according to the order of 0.263 (for MOF-177), 0.16 (for MOF200) and 0.137 (for NEW-MOF), mainly due to reduced packing density of the active sites in the MOFs with larger linkers. The most negative binding energy was also tabulated for the perpendicular approaching of H2 molecules to the node of the central phenyl ring with the bonding distance of 3.19 Å from the linker.