This paper proposes and investigates a distributed adaptive contention window adjustment algorithm based on the transmission history for wireless LANs called the transmission-history-based distributed adaptive contention window adjustment (THAW) algorithm. The objective of this paper is to reduce the transmission delay and improve the channel throughput compared to conventional algorithms. The feature of THAW is that it adaptively adjusts the initial contention window (CW_init) size in the binary exponential backoff (BEB) algorithm used in the IEEE 802.11 standard according to the transmission history and the automatic rate fallback (ARF) algorithm, which is the most basic algorithm in automatic rate controls. This effect is to keep CW_init at a high value in a congested state. Simulation results show that the THAW algorithm outperforms the conventional algorithms in terms of the channel throughput and delay, even if the timer in the ARF is changed.