In this letter, we propose a novel IEEE 802.11 WLAN based MAC to achieve fairness and efficiency for large groups of users. Unlike the current MAC, the proposed scheme excludes nodes which had an access to the channel recently from the contention by controlling a value of CW. The proposed scheme does not only improves throughput performance by reducing contention effectively but also realizes access fairness regardless of the number of contending users. The simulation results show that the proposed scheme can be a nice alternative for future MAC under large population of users.