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Recently, the rapid development of wireless networks and multimedia communication techniques provide solutions to achieve watching digital videos on hand-held devices. Motion estimation (ME), the most important part of video coding, has been used to increase the effectiveness of video compression. However, the computations of motion estimation could be failed in limited computing environments even using the fast algorithms. Therefore, the traditional ME algorithms cannot directly applied to the hand-held devices. In this paper, we propose a partial distortion scheme that sacrifice little visual quality for hand-held devices in a given computation constraint condition. We also analyze various computation-aware based block matching algorithms and present an efficient method to compute the motion vectors. The proposed method significantly reduces the requirement of computation power in computing motion vectors while the number of search points needed is only 25% of the conventional method.