This invention is a process for oxidizing an organic compound with a hydrogen peroxide solution produced by reacting hydrogen and oxygen in the presence of an oxidation catalyst. The hydrogen peroxide is produced by reacting hydrogen and oxygen in a solvent in the presence of a H.sub.2O.sub.2-producing catalyst comprising a polymer-encapsulated combination of a noble metal and an ion-exchange resin. Polymer encapsulation of the H.sub.2O.sub.2-producing catalyst improves its productivity in making hydrogen peroxide and is expected to reduce metal loss.