The electron structure of barium's VIB compound is not clearly known yet. The main problem is that not only the band gap calculated by using DFT (density functional theory) has a large discrepancy compared with experimental results,but also the theoretical values of band gap are inconsistent for different research groups.In order to resolve these problems, this paper makes the Green function-screened coulomb interaction quasiparticle theory(GW) calculation to get the quasiparticle band structure of BaSe.For the convenience of comparison, it deals with the systematic calculation of the energy band of BaSe by using the methods of local density approximation (LDA) and the generalized gradient approximation(GGA). The result shows that the methods LDA and GGA can not describe the band gap of the material accurately, because the calculation errors are as high as 39.9% and 32.6%, respectively. However, the result of quasiparticle band gap by GW improves the band gap value greatly and give the theoretical result which agrees with the experimental measurement. At variance with the known result, BaSe of quasiparticle band gap in the B1 structure is shown to have a direct gap at the Γ-point in the present paper,which indicates that it is important to take into account the 4d electronic effect in the valence electron configuration of barium.