Based on vector wave aberration theory, this paper analyzes the relative positions of the third-order coma node and astigmatism nodes under pupil decenter and proposes an initial structure selection criterion in which the coma node coincides with the geometric midpoint of the two astigmatism nodes. Using this criterion, an F/6 off-axis catadioptric telephoto optical system with a focal length of 900 mm and an entrance pupil diameter of 150 mm was designed. The measured on-axis RMS wavefront error was better than 0.025λ at 632.8 nm. The results demonstrate that the system meets the requirements for high-resolution long-focal-length imaging.