First-principles plane wave calculations predict that Li can be adsorbed on graphene forming a uniform and stable coverage on both sides. A significant part of the electronic charge of the Li 2s orbital is donated to graphene and is accommodated by its distorted π* -bands. As a result, semimetallic graphene and semiconducting graphene ribbons change into good metals. It is even more remarkable that Li covered graphene can serve as a high-capacity hydrogen storage medium with each adsorbed Li absorbing up to four H2 molecules amounting to a gravimetric density of 12.8 wt %.