Miniature batteries can accelerate the development of mobile electronics by providing sufficient energy to power small devices. Typical microbatteries commonly use thin-film inorganic electrodes based on Li-ion insertion reaction. However, they rely on the complicated thin-film synthesis method of inorganics containing many elements. Graphene, one atomic layer thick carbon sheet, has diverse physical and chemical properties and is compatible with conventional micron-scale device fabrication. Here, we study the use of chemical vapor deposition (CVD) grown monolayer graphene in a two-dimensional configuration, as a future Li-oxygen microbattery cathode. By maximizing the dissolution of discharge intermediates, we obtain 2610 Ah/g graphene of capacity corresponding to 20% higher areal cathode energy density and 2.7 times higher cathode specific energy than that can be derived from the same volume or mass of conventional Li-ion battery cathode material. Furthermore, a clear observation on the discharge reaction on composite electrodes and their role in the charging reaction was made, thanks to the two-dimensional monolayer graphene Li-oxygen battery cathode. We demonstrate an easy integration of two-dimensional CVD graphene cathode into microscale devices by simply transferring or coating the target device substrate with flexible graphene layers. The ability to integrate and use monolayer graphene on arbitrary device substrates as well as precise control over a chemical derivation of the carbon interface can have a radical impact on future energy-storage devices.