The electronic structure in UV-VUV region of PbWO4 crystals is studied in a molecular-cluster model within the framework of the fully relativistic self-consistent Dirac-Slater theory, using a numerical discrete variational (DV-X alpha) method. From the calculation, the fundamental gap is found to be around 4.4 eV, the top of valence band is formed almost purely by O 2p and has certain Pb 6s component in the band, W 5d is at the bottom of the conduction band, Pb 6s narrow band is just below the valence band. These results are in reasonable agreement with experimental data measured in the fundamental absorption region using VUV synchrotron radiation.