Zero correlation zone (ZCZ) aperiodic complementary sequence (ZACS) sets have potential applications in multi-carriers (MC) CDMA communication systems, which can support more users than traditional complementary sequence sets. In this letter, methods for constructing ZACS sets based on orthogonal matrices are proposed. The new constructions may propose ZACS sets with optimal parameters. The new ZACS sets can be applied in approximately synchronized MC-CDMA to remove interferences.