Motion estimation and compensation techniques are widely used for video coding applications but the real-time motion estimation is not easily achieved due to its enormous computations. In this paper, a new fast motion estimation algorithm based on line search is presented, in which computation complexity is greatly reduced by using the line search strategy and a parallel search pattern. Moreover, the accurate search is achieved because the small square search pattern is used. It has a best-case scenario of only 9 search points, which is 4 search points less than the diamond search algorithm. Simulation results show that, compared with the previous techniques, the LSPS algorithm significantly reduces the computational requirements for finding motion vectors, and also produces close performance in terms of motion compensation errors.