Existing fast block motion estimation algorithms, which try to reduce the number of search points, utilize the motion vector (MV) characteristics of high spatial correlation as well as center-biased distribution, in predicting an initial MV. Even though they provide good performance for slow motion sequences, they suffer from poor accuracy for fast or complex motion sequences. In this paper, we propose a new fast and efficient block motion estimation algorithm. The proposed algorithm utilizes a new predictor obtained from one-dimensional feature matching based on selective integral projections. This low complexity procedure enables the selection of a better initial search point so that a simple gradient descent search near this point may be enough to find the global minimum point. Compared with recent fast search algorithms, the proposed algorithm has lower computational complexity and provides better prediction performance, especially for fast or complex motion sequences.