Without limitation on the number of mates, Z-periodic complementary sequence (ZPCS) sets, which have potential applications in multi-carriers CDMA communication systems and MIMO channel estimation, can support more users than conventional complementary sequence sets. In this paper, a generic construction of ZPCS sets is proposed based on perfect sequences and orthogonal matrices. It generalizes the earlier constructions by Li et al., and produces new ZPCS sets which cannot generated by earlier ones. The parameters of our ZPCS sets are flexible and are thus suitable for different application scenarios.