In order to simulate dynamic scenes with high accuracy and high reliability, a short-wave infrared (SWIR) and mid-wave infrared (MWIR) multiband catadioptric common-aperture optical system is designed. The system combines the advantages of reflection, refraction, and common-aperture optical paths. The system includes a main optical system, a short-wave optical system and a mid-wave optical system, all designed independently. The initial structure of the optical system is obtained according to theoretical calculation, and the optical parameters are further detailed by optical design software. Finally, the sub-systems are combined according to the principle of pupil matching. The system’s image quality is further optimized, and the system design's rationality is verified by the simulation of the modulation transfer function (MTF) and distortion. The designed short-wave optical system has a field angle of ±0.107°, a focal length of 2500 mm, an entry pupil size of 300 mm, an MTF that reaches the diffraction limit, and less than 0.3% distortion. The mid-wave optical system has a field angle of ±0.65°, a focal length of 750 mm, an entry pupil size of 300 mm, an MTF closes to the diffraction limit, and less than 1% distortion. The system has good image quality, small size and strong practicability. It has great application potential in the field of photoelectric tracking and space detection.