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In this paper, we propose a two-level quality-of-service (QoS) scheduler based on the Ripple medium access control (MAC) protocol to deal with the unfairness problem for a chain-based wireless backhaul network (WBN). A queueing model was first presented to analyze the end-to-end throughput, aggregated throughput, and mean delay of a WBN accommodating single-class traffic. The model was then extended to a WBN with multiple-class traffic-adopting strict-priority (SP) service discipline or weighted-fair-queueing (WFQ) service discipline. Simulation results verified the accuracy of the analysis and the effectiveness of the proposed scheme.