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In video coding standard, motion estimation (ME) always plays an important role in reducing temporal redundancies at the expense of higher computational complexity. Many fast ME algorithms have been proposed to reduce the coding complexity. Some papers focus on applying specific search patterns to reduce the search points within a fixed search range (SR). But there are only a few of them trying to reduce the size of SR. In this paper, an adaptive SR algorithm is presented. Cauchy distribution is used to model the SR for one frame and the information of motion vector differences in the neighboring blocks is used to adjust the SR for a particular block. Experimental results show that the proposed algorithm can reduce the size of SR significantly with negligible quality degradation.