Reflective optical systems have small size,lightweight,and excellent imaging performance,which make it very popular in airborne field. A nonlinear equation group was built based on the matrix optics theory,the initial construction parameters of the optical system can be obtained by deriving this equation group. And during the design process,decenters and tilts of mirrors were adjusted continuously to eliminate the obscurations. the free-form surface was introduced to improve the balance capacity of optical aberration and enhance system field of view. Then an off-axis four-mirror optical system with effective focal length of 100 mm,FOV of 20°×20°,and relative aperture as F/7 is designed. This system has large imaging field of view,tight structure,acentric obstruction and imaging qualities approaching diffraction limit.