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In the upcoming video coding standard, MPEG-4 AVC/JVT/H.264, motion estimation (ME) is allowed to use seven kinds of block sizes to improve the rate-distortion performance. This new feature has achieved significant coding gain compared to coding a macroblock (MB) using fixed block size. However, ME is computational intensive with complexity increasing linearly to the number of allowed block sizes. In this paper, a combined fast motion estimation algorithm with Predict Hexagon Search (PHS) and Edge Information Mode Decision (E1MD) is proposed. EIMD uses the edge information to predict the best matching block size. It can determine the best MB type quickly. The PHS can search the candidate MV efficiently. The analysis results show that the speed improvement of our proposed algorithm over some popular fast motion estimation algorithm is about 2~15 times. Compared with JM10.2, the speed-up is marvelously enhanced as 20~40 times and can still keep good quality as JM10.2.