A design method of elliptical window optical system is proposed and it is based on the fixed aspheric corrector. The algebraic expression of the fixed aspheric corrector is given combining the generalized Coddington equation and the theory of geometric optics. In addition, eliminating astigmatism and sine condition are taken as evaluating parameters, aspheric surface equation is fit by least square method to eliminate astigmatism and coma. Zernike polynomials is used to replace traditional merit function in order to overcome slow convergence in traditional design method of elliptical window optical system. The athermalization of elliptical window optical system is realized by comparing matches of different materials. A complete design example of elliptical window optical system is demonstrated and the results show that the MTF of optical system approaches the diffraction limit across the entire scanning field.