In this paper, we propose a novel inner search algorithm for fast motion estimation to speed up the coding of video compression. The proposed algorithm, called as one-point hexagonal inner search (OPHIS), is based on the characteristic of monotonically decreasing of distortion on a local area. The most probable inner point is checked when an inner search starts. Compared with the enhanced hexagon-based search algorithm (EHEXBS), the OPHIS not only decreases the number of search points but also gets a better video quality. Experimental results show that the speed improvement is about 12.06% on average and the percentage decrease of the mean squared error is near to 2.29% on average. Therefore, the proposed OPHIS is more suitable for the applications of fast motion estimation than the EHEXBS.