In this paper, a novel MAC scheme referred to as P-EDCA is proposed to resolve the unfairness problem in IEEE 802.11e WLANs (i.e., the flows with lower priorities can not get any throughput of data transfer in cases of heavy network loads). P-EDCA provides weighted fairness for differentiated service between the flows, and supports the stations with the 802.11e based multi-queue structure. By using the inner centralized queuing discipline, P-EDCA guarantees fair transmission opportunity between the queues within a station. And by using a contention based access method, i.e., the DFS algorithm, fairness of channel accessing between the stations is reached. Simulation results show that weighted-fair differentiation is accurately implemented by P-EDCA with no information shared between the users. And, without decreasing the performance of higher priority flows, P-EDCA outperforms the original EDCA in terms of its QoS assurance for lower priority flows in the network.