One set of infrared optical system which was based on a 360° continuous-scan focal plane array was realized. This optical system contained one afocal telescope, one compensation scan-mirror, and one re-imaging object lens. A cooled focal plane array sensor was utilized. The scan-mirror was used for azimuth compensation. It scaned at a special angular velocity according to the double angle relationship in the opposite direction, thus the system could solve the problem of image smear. Image space scanning was adopted by the system, thus the size of the scan-mirror can be reduced from about 40 mm×210 mm under object space scanning to 14 mm×22 mm now, and the weight of the scan-mirror could be reduced by more than 95%. Now the swing frequency could reach 100 Hz, which enabled the system to finish 360° azimuth-scan in one second. This system was succinct and compact. It contained eight pieces of lens and one piece of reflective mirror. The image quality was close to the diffractive limit. The laboratory test result shows that, when the scan-mirror is fixed, the image of the small circle hole is blurred, and has smear ghost phenomenon. After the scan-mirror compensation, the image of the circle hole is clear and without smear or distortion, and the image quality is similar to that of the starring system.