In recent years, freeform surfaces have been used increasingly in off-axis reflective imaging systems with high performance levels. In this paper, the cooled off-axis reflection optical system with both a large FOV(field-of-view) and a large relative aperture was designed based on the initial structure from vector aberration theory and genetic algorithm, by using a biased input field and an offset aperture stop, utilizing freeform surfaces described byXY polynomials to increase degrees of freedom to correct off-axis aberrations. The working band of the system was LWIR(long wavelength infrared) 8-12 μm, the focal length was 400 mm, the F-number was 2, the FOV was $ 8^{\circ} \times 5^{\circ} $, and the average root mean square (RMS) wavefront error of the system was 0.037 054λ(λ=9 μm).The detector''s cold stop matches the exit pupil of the optical system which ensure a 100% efficiency of the cold diaphragm. The system has a high energy concentration and a good image quality.