To address the demand for rapid profile inspection of a large number of curved-surface components during aircraft assembly, the research team proposed an automated measurement method based on a laser tracking scanner. First, the coordinate systems of the measuring equipment and the measured object are aligned using the theoretical positioning points provided by the object model. Second, the measurement path of the equipment is planned according to the requirements of the measured curved-surface features of the object, and the complete feature data of the measured curved-surface of the object are automatically collected. Then, the measured data are finely aligned with the theoretical digital model for a second time. Finally, the deviation of the curved-surface profile is calculated. An experiment was conducted using a large-scale rotating paraboloid with a diameter of 4 meters. The results show that this method significantly improves the level of measurement automation. Compared with the traditional manual measurement method, the scanning efficiency is increased by approximately 30%, and the measurement results are consistent. This study provides strong support for advancing the development of high-efficiency geometric quantity inspection technology for curved-surface components of aviation equipment.