Display omitted •15 metal dimers constructed by 5 3d metals (Fe-Zn) are systematically studied.•The OH group as a ligand significantly improves oxygen reduction reaction (ORR) activity.•Ligand OH weakens the scaling relationship of adsorption free energies of oxygenated species.•The volcanic plot predicts that the optimal overpotential is 0.29 V. Various experimental investigation had proved that metal dimers possess excellent oxygen reduction reaction (ORR) activity compared to single metal atom catalysts, due to the synergistic effect exerted by two metal atoms. However, it is still unclear how the electrocatalytic activity is enhanced in a fundamental aspect. In this study, we systematically investigated five 3d transition metals (Fe, Co, Ni, Cu and Zn) by density functional theory (DFT) to explore the ability of metal dimers to catalyze the ORR. It is found that different combinations of different metal atoms have different adsorption strengths to oxygenated intermediates, which helps to screen suitable catalyst materials. The scaling relationship of the free energy of adsorption of oxygen-containing species was calculated for various metal-dimer systems. The classical volcanic diagram is derived, and it is found that the CoZnOH embedded nitrogen-doped graphene (the overpotential is 0.61 V) shows the best catalytic properties, and it is predicted that when the adsorption free energy of OH is equal to 0.95 eV, the optimal overpotential is 0.29 V. Electronic structure calculations show that the pairing of different metal atoms alters the d-band center which in turn change the adsorption properties and hence ORR catalytic performance.