Long-wave infrared optical system with long focal length has been widely used for the fields of military, industrial, civil, medical and so on. People often pursue the large aperture imaging to obtain better imaging, which makes this kind of optical systems have the characteristics of long focal length, large aperture and wide working band range, and it results in serious aberrations and difficult to correct. In order to reduce the complexity of the structure of infrared optical system, the catadioptric structure design is often used to reduce the total length of the optical system; therefore, based on the structure of two reflection mirrors, the optical system was composed of a set of correcting refraction lens after. Firstly, applying the method of coaxial dual mirror optical structure determining parameters to solve the optical parameters of the primary and secondary lens, and an aberration correction spherical lens group consisting of four refraction lenses is added behind the optical structure, to form the initial structure of the long-wave infrared optical system design with long focal length; and then, applying the three conditions of focal degree distribution, heat aberration dissipation and achromatic dissipation to realize the athermalization design, the optical surfaces of the primary and secondary mirrors applied secondary aspherical to design, and combining with optical design software to build the aberration optimization function of the optical system to optimize the aberration. Finally, applying the design method, a long-wave infrared athermalized optical system with large aperture and long focal length is designed, and the operating band of the optical system is 8~12 μm, the focal length is 800 mm, the full field of view angle is 0.6°, the F number is 2.5, the obstruction ratio is 0.2, the total length of the optical system is 344.62 mm. In the operating temperature range of -40 ℃~60 ℃, the value of modulation transfer function in the full field of view angle is greater than 0.25 at the Nyquist frequency of 20 lp/mm. The designed long-wave infrared and athermalized optical system with large aperture and long focal length has the characteristics of compact structure and is good and stable in imaging performance, and realize the optical passive athermalization design of optical system in the case of operating temperature range of -40 ℃~60 ℃. The design method of long-wave infrared and athermalized optical system with large aperture and long focal length discussed provides a reference method for the design of such optical systems, which is of great significance and has great application value.