This paper provides a construction method of periodic complementary multiphase sequences. The proposed method is based on perfect sequences possessing ideal periodic auto-correlation properties. By interleaving any two different perfect sequences with the same length, a kernel set of periodic complementary sequence with multiphase elements can be generated. Compared with the known periodic complementary binary sequences, the presented periodic complementary multiphase sequences may obtain much more lengths of element sequences, which will assure that the generated sequences can provide a more flexible choice of parameters for communication systems.