We have systematically studied the hydrogen adsorption mechanism, hydrogen dissociation, and diffusion on the high-index experimentally-found Mg(101¯3) surface and made comparisons with the low-index Mg(0001) surface, using density-functional theory calculations. Various possible H adsorption sites and structures on the high-index Mg(101¯3) are considered with H coverage up to eight monolayers. Specifically, the hydrogen adsorption sequence is found to be A1-fcc, A2-fcc, A1-tetra Ⅱ, A2-tetra Ⅱ, A3-fcc, B1-hcp, B2-hcp and B1-octa. The HMgH trilayer with Mg1.60+ and H0.80− is found to be very stable during initial H uptake, while the H electron gain of 0.8 e (i.e., H0.80−) is shown to be a reliable indicator of H-adsorbed Mg(101¯3) stability. Interestingly, on the one hand, H2 dissociation is the role step during H uptake on Mg(101¯3) with an H2 dissociation energy barrier of 0.87 eV, which is consistent with the value on the low-index Mg(0001) from previous first principle calculations. On the other hand, the H diffusion barriers along the closed-packed planes are lower than those perpendicular to the planes, verifying that more feasible diffusion paths are available on the high-index Mg(101¯3). These theoretical findings rationalize the previous joint experimental finding that the high-index Mg(101¯3) dramatically decreases H sorption temperatures, and provide an H adsorption mechanism on high-index Mg surface very different from that on low-index Mg(0001), thus improving the foundation of Mg-based hydrogen storage material designs.