The dissociation of a hydrogen molecule on MgO(001) films deposited on Mo (001) surface is investigated systematically using periodic density-functional theory method.The unusual adsorption behavior of heterolytic dissociative hydrogen molecule at neighboring surface oxygen and surface magnesium, is clarified here. To my knowledge, this heterolytic dissociative state has never been found before on bulk MgO(001) or metal supported MgO(001) surfaces. The results confirm that, in all cases, the heterolytic dissociation is much more favorable that homolytic dissociation both energetically and kinetically. The energy difference between two dissociative states are very large, in the range of 1.1 eV ~ 1.5 eV for Mo supported 1 ML ~ 3 ML oxide films, which inhibits, to a great extent, the homolytic dissociation in the respect of reaction thermodynamics. The energy barrier of heterolytic dissociation are about 0.5 eV, much lower that the barrier of homolytic dissociation. The transformation reaction on thick films will be more endothermic. Passing through heterolytic dissociation state have significantly lowered the reaction heat and the energy barrier for obtaining homolytic dissociative structure, which make the homolytic splitting of H2 easier on 2 ML oxide films. The results provides a useful strategy for enhancing the reactivity of the nonreducible metal oxide.