First-principles calculations based on density functional theory and Grand Canonical Monte Carlo (GCMG) simulations are carried out to study the structure of a new Aluminum Metal-Organic Framework, MOF-519, and the possibility of storing molecular hydrogen therein. The optimized structure of the inorganic secondary building unit (SBU) of MOF-519 formed by eight octahedrally coordinated aluminum atoms is presented. The different storage sites of H-2 inside the SBU and the BTB ligand are explored. Our results reveal that the SBU exhibits two different favorable physisorption sites with adsorption energies of -12.2 kJ/mol and -1.2 kJ/mol per hydrogen molecule. We have also shown that each phenyl group of BTB has three stable H-2 adsorption sites with adsorption energies between -6.7 kJ/mol and -11.37 kJ/mol. Using GCMC simulations; we calculated the molecular hydrogen (H-2) gravimetric and volumetric uptake for the SBU and MOF-519. At 77 K and 100 bar pressure, the hydrogen uptake capacity of SBU is considerably enhanced, reaching 16 wt.%. MOF-519 has a high gravimetric uptake, 10 wt.% at 77 K and 4.9 wt.% at 233 K. It has also a high volumetric capacity of 65 g/L at 77 K and 20.3 g/L at 233 K, indicating the potential of this MOF for hydrogen storage applications. (C) 2017 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.