The electronic structure in UV-VUV region of PbWO4 crystaly is studied in a molecular-cluster model within the framework of the fully relativistic self-consistent Dirac-Slater theory,using a nu-merical discrete variational (DV-Xα) method.From the calculation,the fundamental gap is found to be around 4.4eV,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 be-low the valence band.These results are in reasonable agreement with experimental data measured in the fundamental absorption region using VUV synchrotron radiation.