This paper presents a method for the automatic design of a special mid-wavelength infrared zoom system in which the positions of both the pupil planes and the image plane are fixed during the zooming process. In this method, the formulas for the desired zoom system are derived to ensure the exact fulfillment of the conditions with three moving components based on Gaussian reduction. A mathematical model is established based on the particle swarm optimization to determine the first-order parameters of the paraxial design. Then, the model is optimized by iteratively updating a candidate solution with regard to a specific merit function that characterizes the zoom ratio, compactness, and aberration terms. In the optimization phase, the physical feasibility is considered as the constraint on the candidate solutions. Using two examples, this work demonstrates that the developed method is an efficient and practical tool for finding a realizable initial configuration of a dual-conjugate zoom system. Since this method is no longer reliant on the traditional trial-and-error technique, it is an important step toward the automatic design of complex optical systems using artificial intelligence.