This paper presents a new block-based motion estimation algorithm that employs motion-vector prediction to locate an initial search point, which is called a search center, and an outward spiral search pattern with motion-vector refinement, to speed up the motion estimation process. It is found that the proposed algorithm is only slightly slower than cross search, but has a peak signal-to-noise ratio (PSNR) very close to that of full search (FS). Our research shows the motion vector of a target block can be predicted from the motion vectors of its neighboring blocks. The predicted motion vector can be used to locate a search center in the search window. This approach has two distinct merits. First, as the search center is closer to the optimum motion vector, the possibility of finding it is substantially higher. Second, it takes many less search points to achieve this. Results show that the proposed algorithm can achieve 99.7% to 100% of the average PSNR of Fs, while it only requires 1.40% to 4.07% of the computation time of FS. When compared with six other fast motion estimation algorithms, it offers the best tradeoff between two objective measures: average PSNR and search time.