We calculate the band structure of BaS using the local density approximation and the GW approximation (GWA),i.e. in combination of the Green function G and the screened Coulomb interaction W. The Ba 4d states are treated as valence states. We find that BaS is a direct band-gap semiconductor. The result shows that the GWA band gap (Eg-Gw = 3.921 eV) agrees excellently with the experimental result (Eg-EXPT = 3.88 eV or 3.9eV).