By means of density functional theory calculations, the reaction mechanisms of H 2 O 2 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 H 2 O 2 synthesis, which include two hydrogenation and three decomposition steps of key species, are a function of reaction energies, which observe the Brønsted-EvansPolanyi 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 H 2 O 2 synthesis by the reaction energies but also predicts the catalytic performances of Au nanoparticles applied in real catalysis.