For purpose of improving the accuracy and speed of extracting fringe center of linear structured light, an algorithm based on two-terminal prediction and center intersection interpolation is proposed. Firstly, the extraction region is determined by contour tracking and connected domain analysis algorithm to speed up the calculation and reduce the interference of background information. The center was extracted by gray gravity center method, and the curves were fitted to the extracted results. Then, from the center point of the linear structured light fringe to both ends, the initial extraction is carried out: the distance from the extraction point to the fitted curve is calculated, and the average distance is taken as the threshold, and the two-terminal prediction is used when the distance is greater than the threshold. Then, the normal direction of each position of line structure light fringe is calculated by block principal component analysis method, and the interpolation point is obtained by central intersection interpolation method. Finally, the gray gravity center method is applied to the interpolation points to obtain the accurate fringe center coordinates of line structure light. The experimental results show that the proposed algorithm can accurately extract the fringe centers of linear structured light at places with large curvature changes and strong reflections. When extracting the fringe centers of linear structured light generated by computer simulation, the extraction accuracy of the proposed algorithm reaches 64.1 times that of the gray gravity center method and 6.0 times that of the Steger Algorithm, and the running speed of the proposed algorithm is slightly slower than that of the gray gravity center method and 7.6 times that of Steger algorithm.