An asymmetric zero correlation zone (A-ZCZ) sequence set can be regarded as a special type of ZCZ sequence set, which consists of multiple sequence subsets. Each subset is a ZCZ sequence set, and have a common zero cross-correlation zone (ZCCZ) between sequences from different subsets. This paper supplements an existing construction of A-ZCZ sequence sets and further improves the research results. Besides, a new construction of A-ZCZ sequence sets is proposed by matrices transformation. The obtained sequence sets are optimal with respect to theoretical bound, and the parameters can be chosen more flexibly, such as the number of subsets and the lengths of ZCCZ between sequences from different subsets. Moreover, as the diversity of the orthogonal matrices and the flexibility of initial matrix, more A-ZCZ sequence sets can be obtained. The resultant sequence sets presented in this paper can be applied to multi-cell quasi-synchronous code-division multiple-access (QS-CDMA) systems, to eliminate the interference not only from the same cell but also from adjacent cells.