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The channel bandwidth variation and the disconnection during handoff are the most critical problems which degrade the video quality in wireless video streaming. To cope with these problems, we propose an efficient video streaming method in this paper, which does not only dynamically adjust the video transmission rate based on the channel bandwidth, but also minimize the error propagation during handoff. First, the channel bandwidth of the mobile worldwide interoperability for microwave access, called WiMAX, is estimated by analyzing channel parameters including the carrier to interference and noise ratio (CINR) and the handoff is detected by using the handoff occurrence message (HOM). Second, the streaming server adjusts the next transmission rate according to the estimated channel bandwidth to avoid the network congestion and performs the intra refresh method that inserts an intra frame (l-frame) right after handoff by using the HOM to reduce the error propagation effectively. Experimental results indicate that the proposed method can improve the performance of the video streaming over mobile WiMAX.