Cooled detectors have the advantages of high sensitivity, fast response, and long detection distance as compared with uncooled detectors. Therefore, cooled detectors are widely used in infrared optical systems. To effectively suppress stray light, the cold stop of cooled detectors must be at the real exit pupil position of optical systems. In this study, a method for designing cooled off-axis reflective optical systems is proposed. In particular, an unobscured design is achieved by using an offset aperture stop and a biased input field. The initial configuration of cooled off-axis reflective optical systems is directly obtained based on vector aberration theory. A freeform-surface off-axis three-mirror optical system is designed for a long-wave infrared cooled detector that meets the cold stop matching condition. The F number of the designed optical system is 2.5, the focal length is 300 mm, and the field of view is 3°×5°. Freeform surfaces are used to correct the aberrations of the designed optical system and ensure that the designed system has a good imaging quality. The mirrors are free from tilts and decenters, making the designed optical system to be easily aligned.