In order to overcome the difficulty of traditional aspherical surfaces in the structural design of optical systems that cannot simultaneously meet the requirements of imaging quality and system volume, a free-form surface is used to optimize an off-axis two-mirror afocal system.Based on the vector aberration theory, the aberration distribution formula of the system is derived when the free-form surface is at two different positions of the aperture diaphragm and deviates from the aperture diaphragm.Based on this, the Zernike items are selectively introduced to balance the aberration, and the selection of balance parameters for different types of aberrations is discussed in detail.Using this method, a miniaturized infrared off-axis two-mirror afocal system was designed, obtain an optimization result with an entrance pupil diameter of 200mm, a wavelength range of 2.4μm to 3.0μm, the magnification rate of 5, the FOV of 0.4°, and the maximum wavefront RMS is 0.0682λ(λ=2.7μm), the average value is 0.0291λ.Compared with traditional quadratic surface design scheme, the wave aberration has been significantly improved, and MTF has been significantly improved in mid to low frequencies, approaching the diffraction limit in the full field of view.