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Electronic structures of PbMo04 crystals containing F-type colour centres with the lattice structure optimized are studied within the framework of the fully relativistic self-consistent Dirac-SIater 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 band. The optical transition energies are 2.166eV and 2.197eV, respectively, corresponding to the 580 nm absorption bands in PbMoO4 crystal. The 580 nm absorption band in PbMoO4 is originated from the F-type colour centres.