The density functional theory (DFT) calculations are performed to study the oxygen reduction reaction (ORR) on M-N-2-G (M =Ti, Cu, Mo, Nb and Ru) electrocatalyst surfaces. In order to explain catalytic properties of M-N-2-G (M = Ti, Cu, Mo, Nb and Ru) electrocatalysts, adsorption properties of all six intermediates O-2, O, OOH, OH, H2O and H2O2 are analyzed. We also calculate the adsorption property of ORR intermediates on Cu-N-2-G (for example, an ideal catalyst) with the presence of H3O+ ion (acid), OH- ion (base) and water molecule. After analysis, we can see clearly that the stable adsorption site for ORR intermediates in presence of acid, base and water is atop. Moreover, the adsorption properties of ORR intermediates in acid are quantitatively more stable than in base and water respectively. The catalytic activity of the ORR intermediates is found to be enhanced with the increase in the concentration of acid and base, but not of water. Our calculated results reveal that the ORR via a 4 electron transfer mechanism is energetically favorable on the M-N-2-G (M = Ti, Mo, Nb and Ru) electrocatalyst surfaces to form two water molecules, while Cu-N-2-G catalyst surface favors 2 electron transfer pathway to form unwanted hydrogen peroxide. Such types of electrocatalysts will be useful in the practical applications of polymer electrolyte fuel cells. (C) 2017 Elsevier Ltd. All rights reserved.