By interleaving known Z-periodic complementary (ZPC) sequence set, a new ZPC sequence set is constructed with multiple ZPC sequence subsets based on an orthogonal matrix in this work. For this novel ZPC sequence set, which refer to as asymmetric ZPC (AZPC) sequence set, its inter-subset zero cross-correlation zone (ZCCZ) is larger than intra-subset zero correlation zone (ZCZ). In particular, if select a periodic perfect complementary (PC) sequence or PC sequence set and a discrete Fourier transform (DFT) matrix, the resultant sequence set is an inter-group complementary (IGC) sequence set. When a suitable shift sequence is chosen, the obtained IGC sequence set will be optimal in terms of the corresponding theoretical bound. Compared with the existing constructions of IGC sequence sets, the proposed method can provide not only flexible ZCZ width but also flexible choice of basic sequences, which works well in both synchronous and asynchronous operational modes. The proposed AZPC sequence sets are suitable for multiuser environments.