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Video captured from Unmanned Aerial Vehicles (UAV) usually suffer from undesired motion of the sensors, which severely defects detecting and tracking targets of interest. In this paper, a fast video stabilization algorithm for UAV is proposed to remove undesired motions and produce stabilized images. Firstly, a set of fast matching strategies are considered to match successive frames. Then, with motion parameters between two successive frames, a polynomial fitting and predicting method is proposed to estimate the global motion parameters and find out the undesired frames. After that, the undesired images are compensated. Finally, all frames are transformed to obtain stabilized images. Experimental results demonstrate the stabilization and the efficiency of the proposed algorithm.