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In order to guarantee quality of service (QoS) of existing users and to optimize the overall system resource utilization, call admission control (CAC) along with efficient resource reservation scheme plays an important role in next generation wireless networks like WiMax. In prediction based or proactive CAC scheme, new incoming call is admitted or denied based on some predictive or analytical assessment of the user's QoS constraints, wireless channel condition and/or the traffic characteristics. In this paper, we propose a new predictive CAC and resource reservation scheme that predicts the instantaneous new incoming call's QoS requirement using adaptive filtering approach based on the past knowledge gained as well as the QoS trend of the already admitted calls. In our approach, we predict the QoS characteristics of the new calls requiring admission in the network at a predetermined future time. This estimation is based on normalized least mean square (NLMS) adaptive filtering. Based on the estimated characteristic of the future calls and the amount of reserved resource available, instantaneous CAC decision is taken on the new calls and network congestion notification is made and network utilization factor is determined. We have presented computer simulation results to show the effectiveness of our proposed scheme and the efficacy of the different parameters for optimizing the overall CAC and resource reservation process.