Based on the structure of compounding zoom system, a mathematical model of three component continuous zoon design was proposed. Under the guidance of the model, a compact high zoom ratio continuous zoom optical was designed with medium-wave cooling 15μm, 640×512 staring focal plane array. The system works in the range of 3.7~4.8μm and F number is 4. By using this model to distribute the optical power, the initial focal point is calculated to obtain the focal length range of 9~740mm and the zoom ratio is 80×. The whole system used only two kinds of infrared materials of silicon and germanium and eight lenses were used. The system was U-folded by using the secondary imaging and two 45° reflecting mirrors, it effectively achieved 100% cold shield efficiency and controlled the horizontal and vertical dimension. It got the moving lens zoom track and cam curve of each group, and analyzed the continuous zoom optical system from MTF, spot diagram, distortion, narcissus, environment analysis and so on. The design results prove that the zoom system has the advantages of smooth zoom track, great narcissus controlled features and excellent image and it has also been found to apply to infrared imaging system matching with advanced middle wave detector greatly. Finally, the correctness and feasibility of the mathematical model are verified exactly.