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The electronic structures, dielectric functions, complex refractive index and absorption spectra for the PbWO4 (PWO) crystal with and without oxygen vacancy V2O2+ have been calculated using the full-potential (linearized) augmented planewave (FP-LAPW)+local orbitals (LO) method with the lattice structure optimized. The calculated results indicate that the optical properties of the PWO crystal show anisotropy and its optical symmetry coincides with the lattice structure geometry of the PWO crystal. The calculated absorption spectra indicate that the stoichiometric PWO crystal does not display absorption band in the visible and near-ultraviolet range. However, in this range, the absorption spectra of the PWO crystal containing VO2+ exhibit two peaks at 3.35eV (370nm) and 2.95eV (420nm), respectively. It is revealed that the 350nm and 420nm absorption bands are related to the existence of VO2+ in the PWO crystal.