In this paper, a concept of neighborhood for bandwidth allocation and a new bandwidth scheduling scheme are introduced based on two classical scheduling algorithms: round-robin and random choice. The proposed scheme first optimizes the bandwidth scheduling for a subset of Subscriber Station (SS), and then provides the optimal performance based on bandwidth scheduling for the whole WiMAX (world interoperability for microwave access) network, especially in the Mesh mode with step-wise approach. Extensive simulation results using NS2 show that the proposed scheme incurs a short delay and increases system throughput while using the network resource efficiently.