Cr, Ni and Mn are common impurities observed in Al2O3 tritium permeation barrier in experiments, to acquire influence of these metal impurities on the interaction of hydrogen isotopes with α-Al2O3 surface, energies and geometric structures of H2 adsorption, dissociation and diffusion on Cr/Ni/Mn doped α-Al2O3 (0001) surface have been investigated by first-principles. It's found that Cr and Ni have slight effect on H2 adsorption and dissociation on α-Al2O3 (0001) surface due to the similar adsorption and dissociation behavior and close activation energies before and after doping. On Mn doped α-Al2O3 (0001) surface, the adsorption energies for H2 are close to that on undoped surface, while the lowest activation energies for H2 dissociation and H atoms recombination are 0.32 eV and 0.24 eV, which are obviously lower than that for H2 dissociation on undoped α-Al2O3 (0001) surface. This finding reveals that Mn doping is favor to H2 dissociation and also beneficial to H atoms recombination on α-Al2O3 (0001) surface. The lowest activation energy is 1.36 eV for H atom diffusion from surface to bulk on Mn doped α-Al2O3 (0001) surface and obviously higher than that of H diffusion through RAFM steels measured through H2 gas evolution permeation experiment, indicating that Mn surface doping prevents H permeation in Al2O3 tritium permeation barrier from the view of diffusion activation energy. The results are constructive for optimization the preparation technique of TPBs.