The problem of tracking an underwater pipeline (UP) is considered in the context of an inspection mission. It is assumed that the diameter of the cylindrical pipe is known. To solve this problem, a tracking method is proposed, based on searching and calculating the center line of the UP, and determining the relative position of the autonomous underwater robot (AUV) and UP in the coordinate system of the AUV camera. Unlike well-known analogues, in which the solution is based on recognizing and constructing the boundaries of the UP in images, the proposed method searches for the true position of the center line of the UP on a set of possible options by checking their veracity. Possible options for the spatial position of the search centerline of the current UP section are generated by varying the direction of the beam in the horizontal and vertical plane. The starting point of the ray is the end point of the centerline of the previous section. The veracity criterion is to check that the 3D point features constructed in the scene belong to the cylindrical surface of the UP. The generation and matching of pointfeatures in images of a stereo pair is carried out using the SURF detector. The choice of the correct direction of the center line of the current UP section is ultimately made by voting. The end point of the center line of the current section is determined taking into account the calculated common visibility area with the previous section of the UP. To evaluate the effectiveness of the method, computational experiments were carried out on virtual scenes. The effectiveness was assessed by the accuracy of UP localization (in the AUV coordinate system) and by the speed of calculations in comparison with: a) the first version of this method, based on the use of a vectorized form of images; b) analogues using the Canny and Hough Transform detectors. The stability of the method to the accumulation of navigation accuracy errors during long-term tracking of UPs was also assessed.