This paper presents a design method for off-axis reflective zoom optical systems. The method can be used to design off-axis zoom optical systems that include multiple mirrors. First, off-axis spherical systems for different zoom positions are solved to approximately meet the requirements for the optical power at different zoom positions, ensuring the convergence of subsequent calculations. Then, the system's optical power and aberrations are corrected by iterating the freeform surfaces point-by-point, thereby obtaining good starting points for further optimization. To illustrate the effectiveness of the method, three design examples are provided, including two off-axis three-mirror zoom optical systems and one off-axis four-mirror zoom optical system. Using the proposed method, good starting points for these systems are obtained. After optimization, the imaging quality of these three systems is close to diffraction limited.