Minimal path techniques can efficiently extract geometrically curve-like structures by finding the path with minimal accumulated cost between two given endpoints. Though having found wide practical applications (e.g., line identification, crack detection, and vascular centerline extraction), minimal path techniques suffer from some notable problems. The first one is that they require setting two endpoints for each line to be extracted (endpoint problem). The second one is that the connection might fail when the geodesic distance between the two points is much shorter than the desirable minimal path (shortcut problem). In addition, when connecting two distant points, the minimal path connection might become inefficient as the accumulated cost increases over the propagation and results in leakage into some non-feature regions near the starting point (accumulation problem). To address these problems, this paper proposes an approach termed minimal path propagation with backtracking. We found that the information in the process of backtracking from reached points can be well utilized to overcome the above problems and improve the extraction performance. The whole algorithm is robust to parameter setting and allows a coarse setting of the starting point. Extensive experiments with both simulated and realistic data are performed to validate the performance of the proposed method.