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The electronic structures for three types of PbWO4 (PWO) crystals, the perfect PWO, the PWO containing lead vacancy (PWO-VPb) and fluorine doped PWO crystal (F-:PWO), are systematically studied within the framework of density functional theory. The computational results show that the Pb 6s state situates below the valence band so that Pb2+ ions are unable to trap holes forming Pb3+ or Pb4+ to compensate for V2P-b. Thehole-trappers in PWO-VPb are O2- ions. Two of the longer-bond O2- ions share a hole forming O23-, and four of the longer-bond oxygen ions trap two holes forming an associated color centre [O3-2 -VPb-O3-2 ], which may bethe origin of the 420nm absorption band. It is also concluded that the doping of F- would reduce the band gap and F- ions substituting for O2- can effectively restrict the formation of [O3-2 -VPb-O3-2] and weaken the 420nm absorption band and hence enhance the scintillation property of PWO.