A design method of Wasserman-Wolf surfaces is proposed, and it can be used for non-rotationally symmetric catadioptric system. The method is used to design an elliptical dome optical system with compact structure and small volume. Least square method is used to make the initial structure of the system concern the aberration-corrected need of each scanning field. It is beneficial to overcoming the disadvantage that the system evaluation function is difficult to convergence when the entire scanning field is expanded from zero field of regard with respect to calculating and correcting the initial parameters of the components. In addition, the aberration properties of plane-symmetry mirrors with the vector aberration theory of plane symmetry are analyzed and principle by using tilt mirrors to compensate the dynamical aberration in different scanning fields is expounded. At last, a design example of mid-wave infrared elliptical dome optical system is demonstrated, and the results show that the modulation transfer function (MTF) of the optical system approaches the diffraction limit across the entire scanning field.