In order to solve the limitations of existing optical systems in airborne and other fields，optical free-form surfaces with rich degrees of freedom are introduced to design a small F number，large field of view，and lighter airborne mid-wave infrared off-axis two-mirror optical system. The reflective optical system is adopted to eliminate light occlusion by off-axis，and the free-form surface expressed by XY polynomials effectively balances the advanced aberrations by using the first 6 terms. Finally，a medium-wave infrared optical system with a focal length of 240 mm，a field of view angle of 3.8° and an F number of 3 is obtained，and the system's Modulation Transfer Function（MTF）is close to the diffraction limit in the full field of view，and the radius of the Root Mean Square（RMS）of each field of view is within 15 μm of the cell size of a single detector，and the overall physical size is less than 190 mm（X）×190 mm（Y）×240 mm（Z）. The final results show that the system not only meets the imaging quality，but also has simple structure and good lightness，and can be widely used in airborne ground reconnaissance imaging and other fields.