The IEEE 802.11e EDCA (Enhanced Distributed Channel Access) mechanism has been proposed to improve the QoS (Quality of Service) of various services in WLANs (Wireless Local Area Networks). By differentiating the channel access delay depending on ACs (Access Categories), this mechanism can provide the relative service differentiation among ACs. In this paper, we consider that WLAN is deployed in medical environments to transfer medical traffic and we reveal that the quality of the medical traffic (in particular, ECG signals) is significantly deteriorated even with the service differentiation by IEEE 802.11e EDCA. Also, we analyze the reason for performance degradation and show that IEEE 802.11e EDCA has difficulty in protecting the transmission opportunity of high-priority traffic against low-priority traffic. In order to assure medical-grade QoS, we firstly define the service priority of medical traffic based on their characteristics and requirements, and then we propose the enhanced channel access scheme, referred to as DIFF-CW. The proposed scheme differentiates CW (Contention Window) depending on the service priority and modifies the channel access procedure for low-priority traffic. The simulation results confirm that the DIFF-CW scheme not only assures the QoS of medical traffic but also improves the overall channel utilization.