Among various metal/air batteries, lithium-air batteries possess the highest theoretical gravimetric energy density. However, for the rechargeable Li-air battery, besides the challenges of cost, another issue that has to be addressed in the current technology is the limitations of oxygen reduction reaction (ORR) during discharging process and oxygen evolution reaction (OER) during charging process. The sluggish kinetics of the ORR and OER in Li-air batteries is ascribed to the low efficiency of catalysts. Therefore, the design of a low-cost and stable bifunctional electrocatalyst is a major challenge to the construction of efficient Li-air batteries. Several nanocomposite bifunctional catalysts with low cost have been developed in our lab and studied for lithium-air battery applications. In particular, the ORR/OER properties of graphene-Co₃O₄ nanocomposite catalyst have been systematically studied. It demonstrates an excellent catalytic activity toward oxygen reduction reaction including a much more positive half-wave potential (-0.23V) than the pristine graphene (-0.39V) as well as higher cathodic currents. Importantly, this catalyst shows a 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 a Li-air battery. It may be as an alternative to the high-cost commercial Pt/C catalyst for the ORR/OER in alkaline solutions.