Supported catalysts include a solid support such as silica that is functionalized to have inorganic acid functional groups attached thereto. Active catalyst particles are supported on the functionalized support material. The acid functionalized support material is made by reacting a solid support with an inorganic acid containing agent such as sulfuric acid or para-toluene sulfonic acid. An organic anchoring agent is used to form and anchor catalyst nanoparticles to the acid functionalized support material. The supported catalyst can be sized and shaped for use in any type of reactor, including a fixed bed or fluidized bed reactor. The methods of the present invention also include a process for the direct synthesis of hydrogen peroxide using the supported catalyst.