IEEE 802.16 standard was designed to support the bandwidth demanding applications with quality of service .Bandwidth is reserved for each application to ensure the QoS. For variable bit rate applications, however, it is difficult forth subscriber station (SS) to predict the amount of incoming data. The key concern on the bandwidth allocation and scheduling for non real time traffic are the fulfillment of its minimum throughput requirement and improvement of bandwidth utilization with acceptable delay. This paper proposes a simple and efficient scheduling framework for allocating bandwidth to non real time Polling Service (nrtPS) users in IEEE 802.16 grid. In this framework, jointly selective repeat ARQ at the MAC layer and adaptive modulation and coding techniques at the physical are considered. Numerical simulations demonstrate that the proposed scheduling approach provides a graceful compromise between bandwidth utilization and packet delivery delay while maintaining the minimum throughput requirements of nrtPS applications. Thus proves the efficiency of the proposed framework. The simulation is done for unicast scenario.