In the IEEE 802.11 MAC protocol, access points (APs) are given the same priority as wireless terminals in terms of acquiring the wireless link, even though they aggregate several downlink flows. This feature leads to a serious throughput degradation of downlink flows, compared with uplink flows. In this paper, we propose a dynamic contention window control scheme for the IEEE 802.11e EDCA-based wireless LANs, in order to achieve fairness between uplink and downlink TCP flows while guaranteeing QoS requirements for real-time traffic. The proposed scheme first determines the minimum contention window size in the best-effort access category at APs, based on the number of TCP flows. It then determines the minimum and maximum contention window sizes in higher priority access categories, such as voice and video, so as to guarantee QoS requirements for these real-time traffic. Note that the proposed scheme does not require any modification to the MAC protocol at wireless terminals. Through simulation experiments, we show the effectiveness of the proposed scheme.