The Wireless Broadband Network standard IEEE 802.16, popularly referred to as WiMAX is designed specifically to provide differentiated Quality‐of‐Service (QoS) based on the traffic requirement. However the QoS differentiation process is often unfair especially to traffic classes which do not require high QoS guarantee. Such traffic classes are often starved to the extent that they experience extremely low throughput. In this paper, we propose a scheduling algorithm for providing QoS in Wireless Broadband Networks which alleviates the unfairness of IEEE 802.16. The algorithm is primarily based upon two classical queuing principles, namely, Earliest Deadline First (EDF) and Weighted Fair Queuing (WFQ). We propose a service policy which combines the merits of these queuing principles, to mitigate the unfairness posed by IEEE 802.16. Our algorithm ensures that service is not denied to delay tolerant low priority traffic, especially in face of delay intolerant traffic. We simulated the algorithm in dot net framework on the Unix platform using C♯ as the programming language. Our simulation results show considerable improvement in throughput of low priority traffic while retaining the packet delay constraints of the high priority traffic classes.