Based on the principle of compound zoom optical system, a new compound zoom optical system structure is proposed. The structure combines the continuous zoom system with the two-step zoom system to increase the focal length range of the zoom optical system and achieve the larger search range and the longer tracking distance. A mathematical model of optic design of the new compound zoom system is established. Under the guidance of this model, a new compound zoom optical system is designed for long wave infrared uncooled focal plane detector with pixel number of 320×240 and pixel size of 30 μm×30 μm. The working band of the system is 8~12 μm, the focal length range is 10~360 mm, the F number is 2 at 10~60 mm, and the F number is 4 at 60~360 mm. The cam curves and performance of the optical system are analyzed. The results show that the system has such advantages as large zoom ratio, simple structure, good image quality and smooth cam curves, all of which verify the validity of the mathematical model.