The kinetic activation barriers and the thermodynamic free energy changes for the probable elementary reaction steps of oxygen reduction reaction (ORR) are calculated by the first principles methods to clarify the debate whether the 2e(-) or 4e(-) pathway dominates the ORB. on the CoN4 embedded graphene (CoN4-gra). It is found that the CoN4-gra can promote the ORR to proceed along a 4e(-) pathway and to finally generate two H2O by successive hydrogenation reactions. The reduction of OOH into O and H2O with the largest barrier of 0.69 eV is suggested to be the kinetic rate-determining step (RDS). The thermodynamics results show that the elementary steps of ORR along the 4e(-) pathway are downhill at the electrode potential lower than 0.58 V. The last step, the reduction of OH into H2O with the largest Delta G value (-0.58 eV), functions as the thermodynamic RDS of the 4e(-) pathway. The large/small energy barriers and small/large thermodynamic driving forces for the generation/dissociation of HOOH indicate also that the 2e(-) pathway is less favorable than the 4e(-) pathway for ORR on CoN4-gra. (C) 2016 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.