To improve the accuracy of motion estimation in the H.264 video coding, a fractional-pixel motion estimation algorithm is almost mandatory. However, if the image resolution is increased, there is need for additional motion estimation computations that involve considerably more fractional pixels. Therefore, in order to solve the above computational problem, a fast linear-prediction fractionalpixel search algorithm, called FLFS method, is developed in this paper. This FLFS method is based on the linear prediction and a small diamond search algorithm. In addition, the proposed FLFS method substantially reduces the fractionalpixel computations that use the sum of absolute difference error surface. Furthermore, experimental results show that the proposed fast search algorithm can reduce 60% computations for the fractional-pixel calculations and still obtains a good quality of reconstructed video.