Millimeter wave (mmWave) communication is a promising technology to support high-rate (e.g., multi-Gbps) multimedia applications because of its large available bandwidth. Multipacket reception is one of the important capabilities of mmWave networks to capture a few packets simultaneously. This capability has the potential to improve medium access control layer performance. Because of the severe propagation loss in mmWave band, traditional backoff mechanisms in carrier sensing multiple access/collision avoidance (CSMA/CA) designed for narrowband systems can result not only in unfairness but also in significant throughput reduction. This paper proposes a novel backoff mechanism in CSMA/CA by giving a higher transmission probability to the node with a transmission failure than that with a transmission success, aiming to improve the system throughput. The transmission probability is adjusted by changing the contention window size according to the congestion status of each node and the whole network. The analysis demonstrates the effectiveness of the proposed backoff mechanism on reducing transmission collisions and increasing network throughput. Extensive simulations show that the proposed backoff mechanism can efficiently utilize network resources and significantly improve the network performance on system throughput and fairness.