This paper focuses on designing a distributed medium access control algorithm that aims at achieving time fairness among contending stations and throughput maximization in an 802.11 wireless LAN. The core idea of our proposed algorithm lies in that each station needs to select an appropriate contention window size so as to fairly share the channel occupancy time and maximize the throughput under the time fairness constraint. The derivation of the proper contention window size is presented rigorously. We evaluate the performance of our proposed algorithm through an extensive simulation study, and the evaluation results demonstrate that our proposed algorithm leads to nearly perfect time fairness, high throughput, and low collision overhead.