Density functional theory at the B3LYP/6-311??G(d,p) level was used to study the adsorption and dissociation property of a single H 2 molecule on MgB n (n = 2-7) clusters. The hydrogenated structures with lowest-energy of different cluster sizes demonstrate that H atoms prefer to bind with the terminated B atoms with small coordination number by single bond. The structural and electronic stabilities of the hydrogenated clusters were investigated via analyzing the average binding energy, fragmentation energy, second-order energy difference, vertical ionization potential, vertical electron affinity and HOMO-LUMO gap energy. We also explored the feasibility of hydrogenation on B n and MgB n clusters from the viewpoints of thermodynamics and kinetics. The results demonstrate that the adsorption and dissociation of H 2 on the MgB n clusters vary with cluster sizes. H 2 tends to adsorb on the planar boron clusters rather than on three-dimensional boron clusters. Mg doping on B 4 can improve the H 2 storage both in the terms of thermodynamics and kinetic. Moreover, a new bonding way of H 2 with boron clusters was found. Our work provided valuable information for the future boron-based H 2 storage nano-materials.