A hydrophobic composite Pd-membrane catalyst, useful for the non-hazardous direct oxidation of hydrogen by oxygen to hydrogen peroxide, without a gas phase mixing of hydrogen and oxygen or air, having the general formula: HPM (c)/SOMF (b)/M.sub.x Pd.sub.1-x (a)/IPM wherein, IPM is an inorganic porous membrane, M.sub.x Pd.sub.1-x is a metal alloy, permeable only to hydrogen gas, Pd is a palladium metal; M is a metal other than palladium, or a mixture of two or more thereof; x is a mole fraction of the metal M in the metal alloy (M.sub.x Pd.sub.1-x), a, in the round bracket, is a weight of the metal alloy per unit area of IPM; SOMF is a surface oxidized thin metal film comprising palladium b, in the round bracket, is a thickness of SOMF; HPM is a hydrophobic polymer membrane and c, in the round bracket , is a weight of the HPM per unit area of SOMF and a process for producing the said catalyst.