When the infrared search and track (IRST) system is at work, the wide field of view (short focus) is used to achieve the target of wide-area search, and the narrow field of view (telephoto) to achieve the target of location and tracking. Compared with the refractive zoom system, the zoom four-mirror system has compact structure and performs very well at thermalization and achromatism. It can meet the requirements of aerial vehicle IRST temperature adaptability, smaller size and lighter weight. A reflective zoom system design method based on the best least squares method and Seidel aberration is described. Instance is designed to prove the correctness and feasibility of this method. In the process of continuous zoom, the modulation transfer function of this optical system is close to the diffraction limit.