The defects associated with interstitial oxygen in lead tungstate crystals (PbWO4) are investigated by the relativistic self-consistent discrete variational embedded cluster method. The research work is focused on the density of states of interstitial oxygen defects and relational Frankel defects. The transition state method is used to calculate excitation energy of different electron orbits. Simulation results show that the existence of defects related to interstitial oxygen can diminish the bandwidth of the WO2-4 group, and it might produce the green luminescence. Frankel defects associated with interstitial oxygen could result in the absorption at 420nm.