Carbon materials doped with transition metals TM (TM=Fe or Co) and nitrogen (N) have recently attracted much attention as promising electrocatalysts, alternative to precious Pt, for oxygen reduction reaction (ORR) occurring at the cathode of polymer electrolyte membrane fuel cells. Here, we employed the density functional theory calculation method to investigate the progression of ORR on various types of TM-N4 (TM = Fe, Co) moiety substitutionally embedded into a graphene layer. On each possible active site, we calculated the adsorption energies of all the relevant chemical species, namely, O2, O, OH, OOH, HOOH and H2O, and the activation energies for O-O dissociation reactions involved in ORR. Our calculations predicted that the ORR would happen through 4e- associative pathway on FeN4, whereas follow a 2e- pathway on CoN4 site due to high activation energy for O-O bond splitting. These theoretical results are in good agreement with experimental observations.