Abstract: A fast quarter-pixel motion estimation algorithm is proposed in this paper.The proposed algorithm based on mathematical models of the motion compensated prediction errors.Unlike conventional quarter-pixel accuracy hierarchical motion estimation algorithm，proposed algorithm can avoid fractional-pixel interpolation and subsequent fractional-pixel search after integer-pixel accuracy motion estimation.Then a research about the case of optimal integer-pixel on the edge of image is taken.Experiments show that the proposed algorithm greatly reduces the computational complexity of quarter-pixel motion estimation，while keeping the nearly equal quality of the image.