Metal-free catalysts such as non-metal element doped graphene monolayers have attracted considerable interests as the alternative of precious metals for oxygen reduction reaction (ORR) in fuel cells. In this study, the activity of a series of nitrogen (N) and boron (B) co-doped graphene monolayers as metal-free electrocatalysts towards ORR has been explored within the framework of density functional theory (DFT) based calculations. Totally six separate structures containing B and simultaneously, B,N have been constructed with different forms and numbers of N and their performance have been evaluated by calculating the transition states, relative energies and preferred pathways of the ORR. The obtained results in terms of transition states and activation energies clearly underlined the crucial role of pyridinic N in directing ORR towards the efficient 4e(-) pathway with moderate energy barriers and signified the importance of B-N co-doping in the synergistic coupling of opposite effects leading to higher catalytic activity of BN-doped graphene in comparison to singly B-doped one. In addition, the ORR was found to be thermodynamically favorable in the considered structures as the calculated reaction energies at each step of the reactions was exothermic and the energy profile was downhill in all the steps of reactions.