The electronic structures, dielectric functions, complex refractive indices and absorption spectra for a perfect PbWO4 (PWO) crystal and the PWO crystals containing lead vacancy V2-Pb have been calculated using a fullpotential (linearized) augmented plane-wave (LAPW) + local orbitals (LO) method with the lattice structure optimized. The peaks of the absorption spectra corresponding to the electronic transitions have been studied.The calculated results indicate that the absorption band of the perfect PWO crystal does not occur in the visible region. However, the PWO crystal containing V2-Pb has two additional absorption bands in this region. The two bands can be well decomposed into four gaussian-shape bands peaking at 350nm, 405nm, 550nm and 670nm,respectively, which coincide well with the 350nm, 420nm, 550nm and 680nm absorption bands measured in PWO crystals. Therefore, it can be concluded that the 350nm, 420nm, 550nm and 680nm absorption bands are related to the existence of V2-Pb in the PWO crystal.