An ab initio quasi-particle energy band structure for hexagonal boron nitride is calculated with the one-particle many-body Green function approach including core-level electrons. Both the valence and conduction band widths are calculated to be narrow compared with the Hartree-Fock (HF) band width, and the core electron levels are shifted upward from the HF results. The calculated energy gaps from the boron 1s level to several upper valence and conduction levels are found to be close to the results of ESCA, photoemission and electron energy loss experiments.