In order to study the optical properties which are sensitive to the lattice structures for the PbWO4 (PWO) crystal, the electronic structure, dielectric function, complex refractive index and absorption spectra of the perfect scheelite- and raspite-structured PWO crystal have been calculated using linearized augmented plane wave+local obitals (LAPW+lo) method. The peaks of the absorption spectra corresponding to electronic transition and polarization of optical properties have been studied. The optical properties of PWO occur anisotropy. It may be caused by the anisotropy of lattice structure of PWO crystal. The differences of physical property between raspite-structured PWO and scheelite-structured PWO are remarkable. This indicates that the physical properties of PWO crystal are sensitive to the lattice structures. The calculated results provide a theoretical base for further studying the relationship between the optical properties and structures.