Abstract: Based on binary periodic complementary sequence sets, constructions of binary or quaternary periodic complementary sequence sets with Zero Correlation Zone (ZCZ) are proposed. The resultant binary ZCZ periodic complementary sequence set is constructed by interleaving technique and shift sequences. And the resultant quaternary ZCZ periodic complementary set is based on the inverse Gray mapping. If the initial periodic complementary set is optimal, both binary and quaternary ZCZ periodic complementary sets are optimal with respect to the theoretical bound. Moreover, the proposed approach provides flexible choices for ZCZ length.