Accurate acoustic emission (AE) source localization in complex structures remains challenging due to non-straight wave propagation paths and the difficulty of obtaining reliable wave velocity models. To address these issues, this study proposes a velocity-free AE source localization method based on an any-angle pathfinding algorithm. The method integrates the Anya algorithm to estimate geometrically optimal propagation paths and a velocity-free objective function formulated under a weak anisotropy assumption. By avoiding the directional limitations of conventional grid-based pathfinding, the proposed approach provides more accurate distance estimates between potential sources and sensors without requiring prior velocity information. The effectiveness of the method was validated through an AE pulse experiment conducted on a granite specimen containing multiple cylindrical holes. The results demonstrate that the average location error of the proposed method is 19.02 mm, which is less than 38.14 mm of the traditional method and 22.90 mm of the velocity-free method using a grid-based search algorithm. Therefore, the proposed framework is applicable to two-dimensional structures or extruded three-dimensional structures, offering a feasible approach for AE source localization in complex environments.