Two kinds of -Al2O3 materials, with different facet proportions, were carefully prepared by using a template-free solvothermal method. They were used to support Pd catalysts, with varying Pd particle sizes in the range of 0.6-2.6 nm, for the direct synthesis of H2O2 from H-2 and O-2. The evaluation of the catalytic activity and selectivity has demonstrated significant support effects and Pd particle-size effects. The (110) facets predominate the surface of clustered -Al2O3 (-Al2O3-C), while extra (111) facets appear on the surface of nanoplated -Al2O3 (-Al2O3-P), occupying around 30% of the area, in addition to (110) facets. More Pd (100) domains, besides Pd (111), have been disclosed to constitute the surface of small Pd particles deposited on -Al2O3-P, rather than on -Al2O3-C, which has been ascribed to the stabilization of high-energy Pd (100) by dense -OH groups on (111) surfaces of -Al2O3-P. Meanwhile, less PdO species has been found to be present on the Pd/-Al2O3-P catalyst, in comparison with that on the Pd/-Al2O3-C catalyst having parallel Pd particle sizes, suggesting the Pd (100) domains are more resistant than Pd (111) to oxidization. A conceptual illustration has been proposed to explain the effects of the facet orientation of the -Al2O3 support on both the topography of the Pd nanoparticles and the subsequent oxidative species, which are decisive factors for the catalytic activity and selectivity during H2O2 direct synthesis.