In this paper, construction of quaternary low correlation zone (LCZ) sequence sets based on binary sequence sets and interleaving technique is proposed. Some new binary component sequence sets that satisfy specified conditions are constructed compared the known binary component sequence sets. A number of quaternary component sequence sets that satisfy conditions are constructed based on the binary component sequence sets and inverse gray mapping, and then different quaternary LCZ sequence sets can be obtained by these component sequence sets, using the interleaving technique. Therefore, quaternary LCZ sequence sets proposed in this paper can be used in QS-CDMA systems to support more users.