The casings, housings, and complex structural components of the aero-engines pose significant demands for hole machining. However, certain holes are frequently overlooked during CNC programming, resulting in machining discrepancies and delays in production schedules. Consequently, the automatic recognition and programming of holes have become critical challenges for enterprises. To address this issue, a 3D model hole feature recognition method based on graph theory and a feature structure tree is proposed, and an axial priority grouping rule is presented. Initially, hole features are categorized based on the CAD 3D model of the part. A graph structure of geometric elements—including parts, bodies, surfaces, and edges—is constructed using a graph traversal algorithm and feature matching method. Subsequently, geometric information regarding surfaces and edges is extracted using boundary representation, followed by a hierarchical search of surfaces, edges, and adjacent surfaces to construct the feature structure tree for holes. Finally, the path structure tree in the extracted geometric element graph is compared with the predefined types of feature structure tree to ascertain the specific type of hole feature, and the axial priority rule is proposed for grouping. Experimental results from the developed software module show that the recognition rate of hole features reaches 100%, establishing a solid foundation for subsequent hole machining and preventing CNC programmers from missing any holes during programming.