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WiMax system, which is defined by the IEEE 802.16 standard, also called broadband wireless metropolitan area network, supports real time and non-real time services. It has not defined the packet-scheduling algorithms, which was need for the requirement of quality of service (QoS) supporting for real-time services. Generally, the service station (SS) requests for bandwidth from the base station (BS), The BS then allocates the bandwidth to SS according to priority-based request. In this paper we propose a novel bandwidth scheduling algorithm for real time polling services (rtPS), the SS estimate the arrival of rtPS packets prior to the arrival and requests the BS for bandwidth in advance, based on the SS's request and the indeed bandwidth request by past. The analytical model and simulation show that, this adaptive algorithm provided better results with respect to the number of packets waiting at SS and average delay as compared to the widely accepted weighted scheduling algorithm and Mukul 's adaptive bandwidth request mechanism.