The energetically stable structures of M2Hm+ (M = Co, Rh, Ir; m = 2, 4, 6, ...) were investigated using density functional theory calculations, and possible reaction pathways for the sequential adsorption of H2 molecules on M2+ were proposed. Based on the most stable structures, adsorption energies of H2 were calculated for each adsorption step, and the maximum numbers of adsorbed H atoms on Co2+, Rh2+, and Ir2+ were estimated to be 14, 16, and 16, respectively. Compared to group XI elements (M = Cu, Ag, and Au), which are conceivably inert to H2, more H atoms were bound to Co2+, Rh2+, and Ir2+. The adsorption of H2 on M2+ (M = Co, Rh, Ir, or Cu) in the gas phase was investigated experimentally at 300 K using mass spectrometry. Although Rh2+ and Ir2+ stored numerous H2 molecules as predicted by calculations, Co2+ was found to adsorb no H atoms. It was probably due to the insufficient adsorption energy of Co2+ and the kinetic effect in the H2 adsorption process. Thus, computational calculations can overestimate the number of adsorbed H atoms.