Line structured laser three-dimensional (3D) imaging technology has been widely used in welding detection. The fast, accurate, and real-time image extraction of the laser stripe center is the key element for online detection of weld quality under splash interference. Aiming at the problem that the traditional method is difficult to effectively solve the interferences of strong arc light and welding slag spatter, a novel robust and fast laser stripe center extraction algorithm is proposed. First, the geometric center of the stripe is extracted in line with the width constraint of the laser stripe. The fast connected region extraction algorithm is used to screen the effective contour, and the breakpoints caused by splashing are linked by the improved local edge linking algorithm. Second, adjacent contours are searched to create ordered pairs and oriented graphs. The path that has the largest projection length is the real stripe center. Finally, the subpixel center is calculated along the normal direction around the roughly extracting the central contour. The experimental results show that the proposed method can effectively resist spatter interference during welding. The centerline of the light strip can be extracted in real-time and accurately regardless of the removal of the baffle plate of the light sensor. The proposed method has a higher running speed and extraction accuracy compared with some traditional algorithms.