A continuous zoom mid-wave infrared optical system with an F-number of 4 and working wavelength range of 3.7~4.8 μm is designed. To achieve a large zoom ratio, a mechanical compensation method with switching roots has been employed. The narcissus phenomenon is analyzed through simulation, and the zoom curve is optimized. The overall structure of the optical system is compact, and the image remains clear with a smooth curve during the entire zoom process.