It is well-known that the delineated surface water paths (SWP) from a DEM image are essential in hydrology. Both grid-based and contour-based algorithms were proposed in the literature to improve the delineated SWP position’s accuracy. Compared to the grid-based algorithm, the contour-based algorithms usually give more accurate results but require higher computation resources, especially in case of the wide catchment. This paper introduces a new contour-based algorithm which is formulated with the semi-analytical solution of Laplace’s partial differential equation with boundary element method. This approach allows the algorithm to determine the SWP in any direction in order to keep the delineated SWP smooth. The proposed algorithm was validated with the standard synthetic surfaces, where theoretical SWPs are known for accuracy evaluation. The obtained SWPs are more accurate than that of the popular grid-based algorithms. Moreover, the proposed algorithm requires less computation resources when considering very long contour lines. In experimentation with a real DEM image, all delineated SWPs are absolute (no broken part) when the contour interval is equal to or less than 20 meters, and the spacing between adjacent discrete elevation data is 20 meters or narrower. This algorithm helps the hydrologists estimate the catchment area, which is useful for water management in flood and drought prevention.