A particulate supported noble metal phase-controlled catalyst material having 5-1000 μm surface area of 50μ500 m2/gm is provided for use in direct catalytic production of hydrogen peroxide (H2O2) product from hydrogen and oxygen-containing feedstreams. The catalyst is made by depositing phase controlled crystals of a noble metal such as palladium on a suitable particulate support material such as carbon black, by utilizing a precursor solution of the metal and a suitable control ionic polymer having molecular weight of 300-8000 such as sodium polyacrylate in a selected metal to polymer molar ratio of 1:0.1 to 1:10, which procedure provides desired phase control of the noble metal atoms to form widely dispersed minute noble metal crystals on the support material. The invention includes methods for making the catalyst, and also a process for utilizing the catalyst to directly produce high yields of hydrogen peroxide (H2O2) product from hydrogen and oxygen-containing gaseous feedstreams.