The entropy and enthalpy changes upon absorption determine the equilibrium adsorption states, the adsorption/desorption kinetics, and the surface reaction rates. However, it is difficult to measure experimentally or calculate theoretically the entropy of adsorption state. Hydrogen is considered as the most promising candidate to solve the global energy problems, and the storage by adsorption on light porous solids constitutes a main avenue to research field. An ideal storage system should be able to operate under ambient conditions with high recycling capacity and suitable uptake-release kinetics. The entropy of adsorbed H2 molecules is of great significance for determining the optimum conditions for hydrogen storage and for designing the storage materials. To the best of our knowledge, however, the only report on the entropy of the adsorbed H2 molecules is that adsorbed on alkali-metal exchanged zeolites at temperatures around 100 K. Due to different assumptions of the entropy changes, the values of the optimum enthalpy H reported in the publications cover a wide range. In this paper, the adsorption states, vibrational modes, and the entropies of H2 molecules adsorbed on (MgO)9 and (AlN)12 clusters are studied by using first principal method. The computation is performed by the second-order perturbation theory (MP2) with the triple zeta basis set including polarization functions 6-311G(d, p). The very-tight convergence criterion is used to obtain reliable vibration frequencies. Analysis shows that six vibrational modes of the adsorption complexes can be attributed to the vibration of H2 molecule. For these normal modes, the amplitudes of the displacements of cluster atoms are usually two orders smaller than those of the hydrogen atoms. As the vibrational frequency is inversely proportional to the square root of the mass, the zero-point energy has an important influence on the adsorption energy. The ZPE correction exceeds half of the adsorption energy, and the adsorption on the anions is not stable after including the correction. Under the harmonic approximation, the normal vibration modes are independent, so the entropy of adsorbed H2 molecules can be calculated by using the vibrational partition function based on the vibrational frequencies. The results indicate that the entropy values depend mainly on the two lowest in-phase vibrational frequencies and it is not directly related to the adsorption strength but determined by the shape of the potential energy surface. In a temperature range of 70350 K and at a pressure of 0.1 MPa, there is a good linear correlation between the entropy of adsorbed H2 and the entropy of gas-phase. The entropy of H2 decreases about 10.2R after adsorption.