We report an atomistic study based on the pseudopotential Density Functional Theory (DFT) to examine the structural properties and energetics of the molecular hydrogen on imperfect graphene with atomic substitution. The molecular hydrogen adsorption on top, hollow and bridge sites is investigated. On clean graphene, the molecular hydrogen is adsorbed on the hollow site. This is result is in good agreement with available theoretical investigations. The classical Monte Carlo method and Lattice gas Model (LGM) are used to study H-2 physisorption on clean graphene and defected graphene with N, B, Fe and Co substitutional atoms. The semi-empirical Dispersive Force correction (DF) is added to the standard DFT functional in order to capture the essence of Van der Waals (VdW) effects. The modified Lennard-Jones potential is used to fit the obtained DFT DF adsorption energy curves versus the lateral distance between H-2 and graphitic systems. Promising and interesting behaviors for H-2 physisorption on defected graphene with B and Fe are found when compared to clean and defected graphene with N and Co. Copyright (C) 2016, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.