A millimeter-wave (mmWave) wireless system is highly focused as a powerful mean enabling to perform very high data transmission. This paper proposes media access control (MAC) for mmWave wireless system. Existing MAC has limits to achieve high data transmission over 1 - 2Gbps by reasons of low frame transmission efficiency and high overhead of signal exchanges. In addition, the transmitting frames need to be protected in poor channel condition for high quality of service. The proposed MAC provides frame aggregation with unequal error protection (UEP) and block acknowledgement (BIk-ACK) / block negative acknowledgement (BIk-NAK) methods, which can solve the problems of existing MAC and guarantee the high quality of service. Theoretical throughput analysis shows that the proposed MAC has high throughput enhancement compared to the existing MAC and achieves MAC throughput over 2Gbps.