A construction of shift sequence sets is proposed. Multiple distinct shift sequence sets are obtained by changing the parameters of the shift sequences. The shift sequences satisfy the conditions that P|L and P ≥ 2, where P is the length of the shift sequences, L is the length of the zero-correlation zone or low-correlation zone (ZCZ/LCZ). Then based on these shift sequence sets, many shift distinct ZCZ/LCZ sequence sets are constructed by using interleaving technique and complex Hadamard matrices. Furthermore, the new construction is optimal under the conditions proposed in this paper. Compared with previous constructions, the proposed construction extends the number of shift distinct ZCZ/LCZ sequence sets, so that more sequence sets are obtained for multi-cell quasi-synchronous code-division multiple access (QS-CDMA) systems.