In this work, we are evaluating the hydrogen adsorption capacity at 298 K of cobalt-doped MOF-5 using the Grand Canonical Monte Carlo method. We substitute eight, sixteen, and thirty-two zinc atoms of MOF-5 with cobalt atoms and we obtain Co8-MOF-5, Co16-MOF-5 and CoMOF-5 respectively. For each of these molecules, we determine the pore diameters, the surface, the pore volume, the isosteric heat, and the storage capacities of these doped MOFs. The results show that for Co8-MOF-5 and Co16-MOF-5, doping decreases the pore volume and increases the density. This will lead to an increase in volumetric capacity and a decrease in gravimetric capacity. However, we note a strong adsorbent-adsorbate attraction compared to undoped MOF. This is justified by a high excess capacity for materials with a small surface.