Automatic liver segmentation is difficult because of the wide range of human variations in the shapes of the liver. In addition, nearby organs and tissues have similar intensity distributions to the liver, making the liver's boundaries ambiguous. In this study, we propose a fast and accurate liver segmentation method from contrast-enhanced computed tomography (CT) images. We apply the two-step seeded region growing (SRG) onto level-set speed images to define an approximate initial liver boundary. The first SRG efficiently divides a CT image into a set of discrete objects based on the gradient information and connectivity. The second SRG detects the objects belonging to the liver based on a 2.5-dimensional shape propagation, which models the segmented liver boundary of the slice immediately above or below the current slice by points being narrow-band, or local maxima of distance from the boundary. With such optimal estimation of the initial liver boundary, our method decreases the computation time by minimizing level-set propagation, which converges at the optimal position within a fixed iteration number. We utilize level-set speed images that have been generally used for level-set propagation to detect the initial liver boundary with the additional help of computationally inexpensive steps, which improves computational efficiency. Finally, a rolling ball algorithm is applied to refine the liver boundary more accurately. Our method was validated on 20 sets of abdominal CT scans and the results were compared with the manually segmented result. The average absolute volume error was 1.25+/-0.70%. The average processing time for segmenting one slice was 3.35 s, which is over 15 times faster than manual segmentation or the previously proposed technique. Our method could be used for liver transplantation planning, which requires a fast and accurate measurement of liver volume.