Density functional theory and molecular dynamics were used to study the interaction of a lithium atom with a vacancy inside a graphene layer. It was found that the lithium atom is adsorbed on this vacancy, with a binding energy much larger than the lithium cohesive energy. Then, the adsorption of hydrogen molecules around lithium atoms was studied. We found that at 300 K and atmospheric pressure, this system could store up to 6.2 wt.% hydrogen, with average adsorption energy of 0.19 eV per molecule. Thus, this material satisfies the gravimetric capacity requirements for technological applications. A complete desorption of hydrogen occurs at 750 K. However, a multilayer of this system would be required for practical reasons. Under atmospheric pressure and at 300 K, we found that a system made of multiple layers of this material is stable. The storage capacity remained at 6.2 wt.%, but all adsorbed molecules were dissociated. The average adsorption energy becomes 0.875 eV/H. Copyright (C) 2011, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.