Ab-initio calculations are performed to study interaction of hydrogen on aluminum clusters. The results show large binding energies for a single hydrogen atom on Al7 and Al13 and two hydrogen atoms on Al6. The highest occupied-lowest unoccupied molecular orbital (HOMO-LUMO) gaps of Al7 and Al13 become dramatically large by absorbing hydrogen. These large binding energies and HOMO-LUMO gaps make Al7H and Al13H clusters magic(s). The atomic structures and binding energies of Al6H2 and Al8H2 are used to explain the reason why hydrogen is likely to be dissociated only on Al6. These results are discussed in the light of available experimental data and are in very good agreement with them.