A Schmidt optical system consists of a Schmidt corrector plate and a spherical primary mirror, in which the corrector plate lies at the center of the spherical mirror. The focus of the system is not necessarily coincident with the one of the mirror. To precisely find the initial surface parameters of the corrector, a mathematical model based on wavefront aberration functions with the corrector plate surface varying as a function of defocusing amount is established. This model simultaneously corrects both the third-order and the 5th-order spherical aberrations for the system. A Schmidt optical system with aperture size 1000 mm, the mirror radius of curvature 2000 mm and the F number 1 is designed as an example to analyze and test the correctness of the mathematical model of the corrector. The results show that the mathematical model for the corrector agrees with the optimized result of the optical design software Zemax very well. The initial parameters of the optical system are improved greatly. It provided the theoretical foundation of the Schmidt optical systems design with the large aperture and the large relative aperture.