In this paper, we propose an adaptive grey predictor (AGP) that aims at the short-term fading (STF) of noisy Rayleigh channels in the mobile communication systems. Here, we use a moving window to reduce the degradation by the additive white Gaussian noise and further improve the precision of the STF prediction of the adaptive segmental grey prediction model, GM (1, 1, α, β). Computer simulation results show that choosing an appropriate length of moving windows in the proposed window AGP (WAGP) can obtain better accuracy and large performance improvement on the noisy STF prediction.