Electronic structures and absorption spectra for perfect PbWO4 (PWO) crystals and the crystal containing aggregated defect [VP2-Pb-V2+O -VP2-Pb]2- have been calculated using density functional theory code CASTEP with the lattice structure optimized. The calculated absorption spectra of the PWO crystal containing the aggregated defect [VP2-Pb-V2+O -VP2-Pb]2- exhibit two absorption bands peaking at 1.90eV (650nm) and 3.02eV (410 nm). It is predicted that the 420 and 680 nm absorption bands are related to the existence of the aggregated defect [VP2-Pb-V2+O -VP2-Pb]2- in the PWO crystal.