A　facile　hydrothermal　route　has　been　developed　to　prepare　graphene-Co3O4　nanocomposites.　The　graphene-Co3O4　nanocomposite　catalyst　demonstrates　an　excellent　catalytic　activity　toward　oxygen-reduction　reaction　including　a　considerably　more　positive　half-wave　potential　(-0.23　V)　than　that　of　pristine　graphene　(-0.39　V),　as　well　as　higher　cathodic　currents.　More　importantly,　this　catalyst　shows　better　long-term　durability　than　the　commercial　Pt/C　catalyst　in　an　alkaline　solution.　The　preliminary　results　indicate　that　the　graphene-Co3O4　nanocomposite　is　an　efficient　and　stable　bifunctional　catalyst　for　Li-air　batteries　and　may　be　an　alternative　to　the　high-cost　commercial　Pt/C　catalyst　for　the　ORR/OER　in　alkaline　solutions.