Based on the known binary and quaternary zero correlation zone (ZCZ) sequence sets, a class of 16-QAM sequence sets with ZCZ is presented, where the term “QAM sequence” means the sequence over the quadrature amplitude modulation (QAM) constellation. The sequence sets obtained by this method achieve an expansion in the number of 16-QAM sequence sets with ZCZ. The proposed sequence sets can be applied to quasi-synchronous code division multiple access (QS-CDMA) systems to eliminate the multiple access interference (MAI) and multipath interference (MPI) and improve the transmission data rate (TDR).