In IEEE 802.11 standard, the contention window (CW) sizes are not efficient because it does not consider the system load. There has been several mechanisms to achieve the maximum throughput by the optimal CW. But some parameters such as the number of stations and system utilization are difficult to measure in WLAN systems. To solve this problem, we use the network allocation vector (NAV) which represents the transmission of other stations. This parameter can be used to measure the system load. Thus, the CW sizes can be estimated by the system load. In this paper, we derive the analytical model for the optimal CW sizes and the maximum throughput using the NAV and show the relationships between the CW sizes, the throughput and the NAV.