IEEE 802.15.3, an emerging wireless technology, was designed to provide high-quality multimedia services at home. Dynamic bandwidth allocation for a multimedia connection should be considered in order to achieve higher channel utilization, less buffer and less delay, especially for variable bit rate (VBR) multimedia connections. For real-time VBR videos, the bandwidth requirement should be predicted adaptively for effective channel-time requests. Previously, the adaptive least-mean square (LMS) algorithm with fixed step size was applied to predict channel time requirements due to its simplicity and relatively good performance. However, the performance might degrade when scene changes occurred. In this paper, we modify the variable step-size LMS algorithm and apply it as our predictor (VSSNLMS) so that the prediction errors on scene changes can be effectively reduced. Using the prediction results of VSSNLMS, we propose a dynamic bandwidth-allocation scheme that is scene-change aware and can guarantee the delay bound of real-time VBR videos. Simulation results show that the VSSNLMS predictor is superior to previous LMS-type predictors in performance, and the proposed scheme has better performance in channel utilization, buffer usage, and packet loss.