Wireless networks are characterized by bursty and location-dependent errors. Although many fair scheduling algorithms have been proposed to address these issues, most of them assume a simple two-state channel model, where a channel can be either good or bad. In fact, the situation is not so pessimistic because different modulation techniques can be used to adapt to different channel conditions. Multirate transmission is a common technique for wireless networks now a days. This leads to a dilemma: should fairness be built based on the amount of time that a user utilizes the medium or the amount of services that a user receives? In this work, the authors propose a multirate wireless fair queueing (MR-FQ) algorithm that allows a flow to transmit at different rates according to its channel condition and lagging degree. MR-FQ takes both time and service fairness into account. They demonstrate that MR-FQ can guarantee fairness and bounded delays for packet flows by mathematical modeling and analyses. Besides, simulation results show that MR-FQ can also increase the overall system throughput compared to other scheduling methods.