The medium access control of IEEE 802.11e defines a novel coordination function, namely, hybrid coordination function (HCF), which allocates transmission opportunity (TXOP) to stations taking their quality of service (QoS) requirements into account. However, the reference TXOP allocation scheme of HCF controlled channel access, a contention-free channel access function of HCF, is only suitable for constant bit rate traffic. For variable bit rate traffic, packet loss may occur seriously. The authors propose a TXOP allocation scheme to efficiently allocate bandwidth and meet the QoS requirements in terms of both delay bound and packet loss probability. To achieve high bandwidth efficiency, the authors take advantage of not only intra-flow multiplexing gain of traffic flows with large delay bounds, but also inter-flow multiplexing gain of multiple traffic flows with different delay bounds. According to numerical results obtained by computer simulations, the proposed TXOP allocation scheme results in much higher bandwidth efficiency than previous algorithms under the same constraints of delay bounds and packet loss probability.