Based on the most stable structures of the magic MgO clusters, the adsorption of H2 onto the rocksalt and hexagonal tube (MgO)9,12 is studied using first principal method. The results show that physical adsorption can be formed on Mg+q or O-q ions at different sites of the clusters. On the top of the Mg+q ions, H2 is adsorbed in the side-on manner and donates electrons to the ions. On the top of the O-q ions, H2 is adsorbed in the end-on manner and the molecule is polarized. The strength of the adsorption depends mainly on the location of the Mg/O ions, and the smaller the coordination number of the ions, the stronger the adsorption of H2 is. For the Mg/O ions with the same coordination number, the adsorption formed onto the Mg+q is stronger. According to the Mg or O ions and their locations, the adsorption energy ranges from 0.03 eV to 0.08 eV.