The electronic structure of tetrahedrite and effect of four typical natural impurities including zinc, arsenic, iron and silver on its flotation property were systematically studied through density functional theory. The band structure and surface energy calculation show that tetrahedrite is a p-type semiconductor and has no cleavage plane. The frontier orbital energy analysis indicates that compared with chalcopyrite, the flotation separation of tetrahedrite from commonly associated galena, sphalerite and pyrite is more difficult. The Hirshfeld population analysis shows that in comparison with tetrahedrite, chalcopyrite and pyrite, galena and sphalerite have stronger electrostatic attraction to flotation agents, and galena has an obviously better natural floatability than the four other sulfides. The band structure and frontier orbital energy analyses for impurity-bearing tetrahedrites show that they are all p-type semiconductors with better electrical conductivity than pure tetrahedrite, and iron impurity increases the difficulty of tetrahedrite’s flotation separation from galena, sphalerite and pyrite. The Hirshfeld population analysis manifests that zinc and silver impurities enhance tetrahedrite’s electrostatic attraction to flotation reagents while arsenic and iron work in the opposite. Moreover, silver impurity lowers tetrahedrite’s natural floatability while zinc, arsenic and iron have no obvious effects.