Common line-structured light center extraction algorithms have limitations in accuracy and robustness when extracting the center of line-structured light obtained from objects with complex surface structures. In this study, we propose a high-precision center extraction algorithm for multi-curvature line-structured light. This algorithm improves the enhanced parallel thinning algorithm to eliminate redundant points and burrs and fills for missing center points at the end of the light stripe via the improved internal propulsion center extraction algorithm. Finally, sub-pixel centers are recalculated in the direction of the normal vector. A comparative experiment using three classical algorithms was conducted based on a tooth model with a complex curved surface. The experimental results show that the mean absolute error of this algorithm is <0.1, which is only half that of the best-performing dual-threshold grayscale center-of-gravity method in the classical method. Extraction of the center can be performed for multi-curvature line-structured light over 20 curvatures in the range of ( 0.0001 , 4.1439 ) / pixel ^{− 1}; moreover, the end of the light stripe and the identification of the truncation can be improved. Therefore, the proposed algorithm is suitable for contour detection of multi-curvature targets and effectively improves the accuracy of high-precision object detection.