Abstract：With the fast development of mobile Internet, the wireless community has been increasingly looking for a framework that can better provide seamless mobility. Firstly, this paper processed received signal strength smoothly using improved Exponentially Weighted Moving Average (EWMA) algorithm. Then, a fast cross-layer handover scheme based on movement prediction in mobile WIMAX environment was proposed. Prediction is achieved by grey predictive model with keeping track of the signal strength of mobile users. With the help of the prediction, layer-3 handover activities are able to occur prior to layer-2 handover, therefore, total handover latency can be reduced.