In this paper, the authors propose a new class of ternary Zero Correlation Zone (ZCZ) sequence sets based on binary ZCZ sequence sets construction. It is shown that the proposed ternary ZCZ sequence sets can reach the upper bound on the ZCZ sequences. The performance of the proposed sequences set in asynchronous Direct Sequence-Code Division Multiple Access (DS-CDMA) system is evaluated. In the simulation they used two types of channels: Additive White Gaussian Noise (AWGN) and frequency non-selective fading with AWGN noise.