Possible geometrical structure, relative stabilities of Mg3N2Hm(m=1-4) and (Mg3N2)nHm(n=2-4,m=1-2) clusters are studied by using the density functional theory (B3LYP) with 6-311G* basis sets. For the most stable isomers of Mg3N2Hm(m=1-4) and (Mg3N2)nHm (n=2-4,m=1-2) clusters, the electronic structure,bonding characteristics, charge distribution, vibrational properties and relative stabilities are analyzed. When the number of the adsorbed H atoms less than that of N atoms, it mainly forms -NH group. And then some H atoms are adsorbed by the -NH groups and it forms -NH2 groups while some other H atoms are adsorbed by Mg forming MgH when all the N atoms bond as -NH. H atom is easialy adsorped on N atom which is projecting and contains the lone pair electrons. Due to the repulsion between the lone pair electrons, the adsorption positions of H atoms were away from each other. The N-H in cluster showed covalent interaction, where the Mg-H showed ionic bond interaction. The properties of-NH and -NH2 group are consistent with that of crystals, so the cluster can describe the behavior of the hydrogen storage in crystals.