Energies and geometric structures of H2 molecule adsorption and dissociation on Fe doped α-Al2O3 (0001) surface have been investigated by the first-principles calculation since Fe is a common impurity in Al2O3 tritium permeation barrier. It's found that Fe prefers to substitute the surface Al site and the adsorption of H2 on Fe doped α-Al2O3 (0001) surface is physisorption. The adsorption energies and dissociation activation energies of H2 absorbed on Fe doped α-Al2O3 (0001) surface are slight lower than that of H2 on undoped α-Al2O3 (0001) surface. The activation energies of H atoms recombination are 0.65 eV and 0.53 eV and obviously smaller than the values of 0.92 eV and 1.03 eV for H atoms recombination on undoped α-Al2O3 (0001). Therefore, Fe surface doping has slight effect on the reactivity for H2 adsorption and diffusion on α-Al2O3 (0001) surface, but is beneficial to α-Al2O3 as a tritium barrier from the view of H atoms surface recombination.