In an IEEE 802.11 multirate network, the aggregate system throughput is unfavorably dominated by stations with the lowest data rate. To improve the performance, it is required to provide airtime fairness for stations regardless of their data rates. Unfortunately, the IEEE 802.11 MAC protocol DCF (Distributed Coordination Function) fails to satisfy this requirement. In this paper, we propose an adaptive MAC scheme, named Time Fairness Transmission Control (TFTC), to maximize the system throughput while maintaining airtime fairness among the competing stations. Specifically, making use of the information provided to each station by the carrier sensing mechanism, TFTC dynamically adjusts the transmission probabilities for stations transmitting at each data rate. As opposed to the previous works, our proposed scheme has strong ability to lead the network to work under near optimal state without the requirement of estimating the number of active stations in the network. Performance evaluation results show that the scheme is effective in achieving near to the theoretical maximum system throughput and providing time fair channel allocation among stations with different data rates.