The aircraft with an elliptical dome acquires excellent aerodynamic performance, but the non-rotationally symmetric structure characteristic of the dome makes the airborne infrared search/track system difficult to meet the requirements of wide field-of-regard (FOR) and high imaging quality at the same time. In order to overcome this problem, a design method for the elliptical dome optical system based on the combination of an arch corrector and a dynamic corrector was proposed. A mid-wave infrared optical system with an ellipsoid dome was designed as an example. The system has a super wide FOR of ±54°, and the imaging quality of the system approaches to the diffraction limit across the entire FOR and instantaneous field-of-view.