With the accurate ab initio method, the adsorption and dissociation process of H2 molecule on Al7- cluster anion are investigated. The stable structures of molecular adsorption and dissociative adsorption are confirmed. The photoelectron spectra of different structures are further analyzed. The calculations indicate that the adsorption of H2 on Al7- is weak physical adsorption with the adsorption energy about 0.02 eV. The investigation of the dissociation process shows that the energy barrier of dissociation is about 0.75 eV. The densities of states of the Al7- cluster and the dissociative adsorption complex Al7H2- are in good agreement with those obtained by the photoelectron spectroscopy. It suggests that H2 can be dissociated when it is absorbed on Al7- anions produced by laser ablation.