It has been well established that nitrogen coordinated transition metal, TM-N₄-C (TM=Fe and Co) moieties, are responsible for the higher catalytic activity for the electrochemical oxygen reduction reaction. However, the results obtained using density functional theory calculations vary from one to another, which can lead to controversy. Herein, we assess the accuracy of the theoretical approach using different class of exchange-correlation functionals, i.e., Perdew-Burke-Ernzerhof (PBE) and revised PBE (RPBE), those with the Grimme's semiempirical dispersion correction (PBE+D3 and RPBE+D3), and the Bayesian error estimate functional with the nonlocal correlation (BEEF-vdW) on the reaction energies of oxygen reduction reaction on TM-N₄ moieties in graphene and those with OH-termination. We found that the predicted overpotentials using RPBE+D3 are comparable and consistent with those using BEEF-vdW. Our finding indicates that a proper choice of the exchange-correlation functional is crucial to a precise description of the catalytic activity of this system.