In an approximately synchronized (AS) code-division multiple-access (CDMA) communication system, zero correlation zone (ZCZ) sequences can be used as its spreading sequences so that the system suppresses multiple access interference (MAI) and multi-path interference (MPI) fully and synchronously. In this letter, the mutually orthogonal (MO) ZCZ polyphase sequence sets proposed by one of the authors are improved, and the resultant ZCZ sequences in each set arrive at the theoretical bound regarding ZCZ sequences under some conditions. Therefore, the improved MO ZCZ sequence sets are optimal.