The adsorption of H₂ on Zr(0001) crystal surfaces is studied by the first-principles plane wave pseudopotential method within the density functional theory. By calculating the preferred adsorption sites, adsorption energy and electronic structure of Z(0001)/H₂ system, the microscopic mechanisms for adsorption of H₂ on Zr(0001) surfaces was clarified. The results show that the favourable adsorption position of H₂ on Zr(0001) surface is the fcc site and its adsorption energy is 0.899 eV belonging to a strong chemical adsorption, and the two H atoms dissociated from H₂ molecules are finally stably adsorbed at the hollow and fcc sites on the surface of Zr(0001). There is a large amount of charge transfer between the adsorbed H atom and Zr (0001) surface, which results in the formation of ionic bond between H and Zr atom, and the typical covalent bonds between H and surface Zr formed through the orbital hybridization of H1s and Zr5s, 4d. As a result, one can see that the chemical bonding between the H atom and the surface Zr atom is a characteristic mixture of the ionic and covalent bonding. In addition, the adsorption energy gradually increases with the coverage. When the coverage increases to a certain value, half of H atoms are adsorbed on the subsurface.