Graphene is a 2D lattice of Carbon atoms which has a high potential to use it for hydrogen storage. In this paper we have studied theoretically the adsorption of hydrogen molecules on a single-layer graphene and we obtained the adsorption energy including optimized position and orientation of the hydrogen molecule with respect to the graphene surface in different points of the graphene lattice. We have done our calculations using Quantum-ESPRESSO code and applying pseudo-potential method in the framework of Density Functional Theory (DFT). We have used Local Density Approximation (LDA) for exchange correlation energy. Our result shows that adsorption energy is increased with decreasing the density of . However the maximum adsorption energy is occurred on the hollow position and for the surface homogenous arrangement.