Design and development of a single atomic catalyst with high activity is desirable but proved to be very challenging in the renewable energy conversion and storage technologies. As a classic carbon material, graphene has many excellent properties and thus may be a good support to stabilize the isolated metal atoms. However, the oxygen evolution activity of a single cobalt atom supported on graphene is still very low. To improve its performance, support modification has been carried out based on a density functional theory framework for the design predication. In our theoretical study, two nitrogen formats are incorporated to the graphene substrates, including graphitic nitrogen and pyridine-like nitrogen, which are usually observed in experiment. The oxygen evolution process has been envisaged on these single cobalt atom catalysts via gas phase adsorption calculation. The electronic structure on the single Co active site can be effectively regulated by the support modification, which will contribute to its enhanced performance. Henceforth, free energy change diagrams, partial density of states, Raman spectra, and charge density difference are discussed. It is suggested that incorporating pyridine-like nitrogen on graphene is an ideal approach for the supported Co atom to achieve high OER activity, opening up new opportunity for the preparation and application of highly active and stable single atomic catalysts.