Fundamental understanding of the structure sensitivity of Au-catalyzed H2O2 formation from H-2 with O-2 is of prime scientific and industrial significance. Herein, DFT calculations are employed to reveal the underling nature of the site-dependent H2O2 formation activity and selectivity over three typical Au(111), Au(100), and Au(211) sites. The hydrogen dissociation is suggested as the rate determining step. The structural and charge analysis and the energy barrier decomposition indicate one lower-coordinated edge atom on the Au(211) as the active site for hydrogen dissociation. Furthermore, competition reactions between hydrogenation/desorption of the species involving the O-O bonds and their cleavage are comparatively studied. Au(111) is found to exhibit the highest selectivity to H2O2. Finally, a combination of the low-coordinated Au atom with Au(111) is proposed as the catalytically active center of H2O2 formation. The results demonstrated here could be valuable for fabricating highly active and selective catalysts for H2O2 formation.