By means of density functional theory calculations, the reaction mechanisms of H2O2 synthesis on three low index and two stepped Au surfaces have been investigated in detail. This study shows the activation energies of five elementary reaction steps of H2O2 synthesis, which include two hydrogenation and three decomposition steps of key species, are a function of reaction energies, which observe the Bronsted-Evans-Polanyi rules on both the flat Au surfaces and the step edge sites of stepped Au surfaces. This study not only provides a simple method to estimate the reaction barriers of elementary steps of H2O2 synthesis by the reaction energies but also predicts the catalytic performances of Au nanoparticles applied in real catalysis. .