We have performed density functional theorybased first-principles calculations to study the stability, geometrical structures, and electronic/magnetic properties of pure graphene, sodium (Na)-adsorbed graphene and also the adsorption properties of H 2 -molecular ranging from one to five molecules on their preferred structures. Using the information of binding energy of Na at different adsorption sites of varying sized graphene supercell, it has been observed that hollow position is the most preferred site for Na adsorption, and the same in 3 Â 3 supercell has been used for further calculations. The band structure and density of states calculations have been performed to study the electronic/magnetic properties of Na-atom graphene. On comparing adsorption energy per H 2 -molecular in pure and Na-adsorbed graphene, we find that presence of Na atom, in general, enhances binding strength to H 2 -moleculars.