The adsorption properties of hydrogen on the supported-metal surfaces are investigated using the Green function method within the framework of tight-binding approximation. The adsorption energy ΔE and the adatom state energy Ead, for hydrogen adsorption on Pt/ZnO, Cu/ZnO and Ni/ZnO composite systems are calculated by employing the self-consistent An-derson-Newns adsorption theory. The effects of the metal-support interaction on the adsorption properties of hydrogen on supported-metal surfaces are discussed. It is found that the stronger the metal-support interaction is, the less the adsorption energy and charge transfer for H on Pt(Cu,Ni)/ZnO become. The metal-support interaction impedes hydrogen adsorption on the metal surfaces. This effect becomes weak as the metal film grows thick.