With the development and wide application of large area array and high resolution cooled detectors, the requirements for imaging field of view and imaging performance of optical system are becoming higher and higher. Compared with rotationally symmetric spherical and aspheric surfaces, free-form surfaces have higher design degrees of freedom. At present, domestic and foreign scholars mostly use 2-3 free-form surfaces to realize the design of the off-axis three-mirror optical system of free-form surfaces. The optical system configuration is the primary imaging rectangular field of view optical path or the secondary imaging real entrance pupil linear field of view optical path. There are few reports on the design of the secondary imaging real entrance pupil rectangular field of view optical path. To meet the design requirements of wide-band and large-field airborne optical system, a set of off-axis three-mirror optical system for long-wave infrared cooled detector is developed using the form of secondary imaging optical path and XY polynomial free-form surface. In this paper, a fast numerical iterative calculation method based on the aberration equation (Fig.1) is presented. A program is compiled using MATLAB to solve the initial structure of the central field of view based on the Tamer T. Elazary quadratic field vector aberration equation. The field of view is continuously increased for calculation, and a better initial structure is finally obtained. The node aberration optimization method is used to balance the coma and astigmatic node characteristics in the full field of view (Fig.3), and gradually reduce the number of free surfaces. The Monte Carlo algorithm is used for tolerance analysis to determine the reasonable tolerance limit distribution (Tab.1). Finally, the interferometer is used to detect the surface shape of the aspheric and free-form surface components machined by turning (Fig.9).The optimized off-axis tri-reflector optical system contains only one free surface (Fig.4), and the efficiency of the cold diaphragm is 100%. Its field of view reaches 5.5°×4.4°, full field MTF is close to diffraction limit. The maximum RMS of full-field wave aberration is 0.06λ and the minimum value is 0.01λ. The average value of wave aberration is 0.03λ(λ=9.11 μm). The imaging quality of the system is good. The system solves the problem of cold aperture matching and the design difficulty of small meridian field of view for the cooled detector. The system is compact without central barrier. And it has technical advantages of wide band, large field of view, high transmittance, etc. This paper designs an off-axis three-mirror optical system based on the 640×512@24 μm long wave infrared cooled detector. The system adopts the secondary imaging optical path and XY polynomial free surface. The focal length of the optical system is 160 mm, and the working band is 8-12 μm. The F number of this system is 2, and the field of view reaches 5.5°×4.4°. At the same time, this paper also analyzes the tolerance of the reflective free-form surface optical system. The surface shape of the parts was tested after machining. The wavefront test results of the optical system show that the full-field average value of the system wave aberration is 0.067λ(λ= 9.11 μm). The whole system has good imaging quality.