Aiming at the 640×512 cooled medium-wave infrared focal plane detector, the optical structure of secondary imaging and the compensatory zoom mode of mechanical positive group are adopted, and the silicon diffraction optical element is used in the design, so as to form the refractive-diffractive hybrid zoom optical system. The results show that MTF is close to the diffraction limit at the spatial frequency of 33 lp/mm. 7 lenses are used in the optical system, and 15--300 mm continuous zoom is achieved in the band of 3.7--4.8 m. The total weight of the optical lens is only 86 g and the total length of the optical system is 139 mm. The optical system has the characteristics of large multiplier ratio, high resolution, light weight and small size.