In this paper,the way to choose configurations for infrared optical system design was discussed.A compact catadioptric infrared optical system was designed.The ratio of total length and focus length was 0.59.The results show that the system possesses better athermal performances in the temperature range-40℃～60℃.The image quality of the system almost reaches diffractive limit.In addtiton,the optical system has many advantages,such as compact structure,small volume and so on.It can be applied to imaging infrared seeker.