This paper proposes a novel alpha wrapping-based collision-free surface-along path planner (AWP) designed specifically for unmanned aerial vehicles (UAVs) navigating along complex structural surfaces. The major objective is to facilitate collision-free movement of UAVs along such surfaces. The proposed methodology entails three key steps. Firstly, the alpha wrapping algorithm generates a free 3-dimensional curve, which smoothly carves and refines a mesh to approximate the desired structure. This process efficiently creates a free and smooth space for UAV maneuverability. Secondly, the axis-aligned bounding box (AABB) tree is constructed based on the mesh representation of the free space. The AABB tree identifies the points nearest to the UAV’s start and target points within the free space. Lastly, a discrete geodesic problem solver determines the shortest path between the identified nearest points. The discrete geodesic problem solver considers the continuous characteristics of the surface represented by the mesh. The proposed AWP takes advantage of mesh-based path planning, thereby providing UAVs with collision-free surface-along paths. The experimental results demonstrate the proposed method’s efficiency and robustness in generating collision-free paths for UAVs when traversing complex structures.