The experimentally prepared high-index Mg(10 (1) over bar3) is able to lower the H adsorption temperature by 200 K. The potential of hydrogen sorption properties of high-index Mg(10 (1) over bar3) deserves further investigations. In this paper, we conduct first-principles calculations to study the stabilities of transition metal substitution on the conventional low-index Mg(0001) and the experimentally prepared high-index Mg(10 (1) over bar3), including Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Y, Zr, Nb, Mo, Tc, Ru, Rh, Pd, Ag, Cd, Pt and Au. Our results show that Mg(10 (1) over bar3) can stabilize Ni, Zn, Ag, Cd and Au on the outermost layer, while, on Mg(0001), all the TM dopants studied have a lower stability on the outermost layer except Cd than the second outermost layer. This difference is because of charge depletion and charge smoothing effects more obvious in the surface regions of high-index surface. Consequently, substituted TMs on Mg(10 (1) over bar3) exhibit larger atomic displacements toward the bulk region along z axis in order to form bonds with neighboring Mg atoms. Substituted TMs on Mg(10 (1) over bar3) form stronger TM-H bonds compared to Mg(0001). For H-2 dissociation, Ni and Zn are capable of dramatically lowering the energy barrier of H-2 dissociation from 0.90 eV on pure Mg(0001) surface to 0.02 eV on Ni/Mg(10 (1) over bar3) and to 0.39 eV on Zn/Mg(10 (1) over bar3). For H-2 formation, Ni/Mg(10 (1) over bar3) and Zn/Mg(10 (1) over bar3) have energy barriers of 0.41 eV and 0.42 eV, respectively, slightly larger than the pure Mg(10 (1) over bar3) of 0.39 eV. In summary, our thermodynamics and kinetics results imply that Ni- and Zn-substituted high-index Mg(10 (1) over bar3) can be a promising material for hydrogen storage, and open the gate for digging the hydrogen sorption property potential of TM-doped high-index surface.