EEE 802.16 networks are designed based on differentiated services concept to provide better Quality of Service (QoS) support for a wide range of applications, from multimedia to typical web services, and therefore they require a fair and efficient scheduling scheme. However, this issue is not addressed in the standard. In this paper we present a new fair scheduling scheme which fulfills the negotiated QoS parameters of different connections while providing fairness among the connections of each class of ser- vice. This scheme models scheduling as a knapsack problem, where a fairness parameter reflecting the specific requirements of the connections is defined to be used in the optimization criterion. The proposed scheduler is evaluated through simulation in terms of delay, throughput and fairness index. The results show fairness of the scheduling scheme to all connections while the network guarantees for those con- nections are fulfilled.