The current contention mechanism of the IEEE 802.11 distributed coordination function (DCF) is known to have some drawbacks, e.g., collisions and low short-term fairness induced by minimizing the backoff stage after every successful transmission. To solve the drawbacks we propose an adaptive contention window control scheme which uses a single backoff stage while maintaining the advantages of the current IEEE 802.11 DCF such as simplicity and distributivity. We first introduce the key concept called the optimal collision probability and explain the detailed procedure of the proposed scheme which is based on the optimal collision probability. The convergence of the proposed scheme is shown. The validation from simulation results shows that the proposed scheme provides higher throughputs and higher short-term fairness than the IEEE 802.11 DCF.