This paper addresses the QoS support issue of IEEE 802.11e in multirate networks. Prior researches focused on the "performance anomaly" problem without QoS consideration. We show the QoS support is insufficient in the current 802.11e standard and related methods make it worse by using NS-2 simulation tests. We propose a hybrid method that maintains the quality of highest priority traffic and enhance the system performance concurrently. We also compare its performance with other proposed methods. Our results demonstrate that our proposed hybrid method can efficiently support the time constraints of voice flows in various network conditions. Moreover, the system throughput is improved by the hybrid method when compared to the IEEE 802.11e standard.