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Electronic structures of PbWO4 crystals containing F-type colour centres with the lattice structure optimized are studied within the framework of the fully relativistic selF-consistent Dirac-Slater theory, using a numerically discrete variational (DV-Xα) method. The calculated results show that F and F+ centres have donor energy levels in the forbidden bands. Their optical transition energies are 1.84 eV and 2.21 eV, respectively, which correspond to the 680nm and 550nm absorption bands. It is predicted that the 680nm and 550nm absorption banas originate from the F and F+ centres in PbWO4 crystals.