Sequences with some desired correlation properties are useful in communication and radar systems for applications in identification, synchronization, ranging and interference mitigation. This paper put forwards a construction of zero correlation zone (ZCZ) sequence sets with flexible ZCZ based on interleaving technique. Different to traditional interleaving, it designs shift sequences according to the mathematical relations between the length of initial sequence, the length of shift sequence and the ZCZ of the resultant sequence set rather than only considering the length of the initial sequence and the length of the shift sequence. This paper analyses and proves the two shift sequences are equal when they simultaneously satisfy both of the different mathematical relations. This construction enriches quantity of ZCZ sequence sets and is meaningful in the application of quasi-synchronous code division multiple address (QS CDMA) communications.