We present a density functional theory study of the oxygen reduction reaction (ORR) on a single atom catalyst embedded in graphene, namely, TM-N₄-C (TM = Fe and Co), using the effective screening medium method combined with the reference interaction site model (ESM-RISM). It was found that Fe-N₄-C and Co-N₄-C show comparable ORR activities from the constant electrode potential simulations, in contrast to the results obtained using the constant (neutral) charge simulation, in which the superior performance of Co-N₄-C has been predicted. The constant potential method allows the variable charge and thus, resulting in a potential dependence of the reaction free energies different from that with the constant charge method in which the potential dependence is included as an ad hoc manner. We suggest the importance of the variable charge in the simulation of the electrochemical reaction, which is enabled by ESM-RISM.