The electronic structures and absorption spectra for the perfect PbMoO4 crystal and the crystal containing lead vacancy $ {\rm V}^{2-}_{\rm Pb} $ with lattice structure optimized are calculated using density functional theory code CASTEP. The calculated absorption spectra of the PbMoO4 crystal containing $ {\rm V}^{2-}_{\rm Pb} $ exhibit three absorption bands peaking at 2.0 eV (620 nm), 3.0 eV (413 nm) and 3.3 eV (375 nm), which are in good agreement with experimental values. The theory predicts that the 390 nm, 430 nm and 580 nm absorption bands are related to the existence of $ {\rm V}^{2-}_{\rm Pb} $ in the PbMoO4 crystal. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)