The IEEE 802.11e Medium Access Control (MAC) is an emerging standard to support Quality of Service (QoS). Some recent works prove that 802.11e Hybrid Coordination Function (HCF) can improve significantly the QoS support in 802.11 networks. A simple HCF scheduler has been proposed in the 802.11e which takes the QoS requirements of flows into account and allocates time to stations on the basis of the mean sending rate. As we show in this paper, this HCF scheduling algorithm is only efficient for flows with strict Constant Bit Rate (CBR) characteristics. However, several real time applications, such as videoconferencing, may sometimes have small variations in their packet sizes, sending rates or even have Variable Bit Rate (VBR) characteristics. In this paper, we propose a new HCF scheduling algorithm, FHCF, that aims to be fair for both CBR and VBR flows. The FHCF scheme uses queue length estimations to tune is time allocation to stations. We present a set of simulations and provide performance comparisons with other schemes. Our performance study indicates that FHCF provides good fairness while supporting bandwidth and delay requirements for a large range of network loads.