The effect of point defects on the copper (Cu)-related deep levels in p-type Czochralski (Cz) silicon has been investigated. It was found that generally five deep levels Ev+0.14 eV, Ev+0.17 eV, Ev+0.32 eV, Ev+0.35 eV, and Ev+0.46 eV were related to Cu in the p-type Cz silicon. Among them, the newly found levels Ev+0.35 eV and Ev+0.32 eV can be influenced by the point defects introduced during rapid thermal process. The intensity of level Ev+0.35 eV increased with the introduced vacancies, while that of level Ev+0.32 eV was dependent on the silicon interstitials. Moreover, the electronic states of those two levels were ascribed to be localized states. Based on the experimental facts, it is believed that the origins of levels Ev+0.35 eV and Ev+0.32 eV are the complex of Cu and vacancy and that of Cu and silicon interstitials, respectively.