The astronomical telescope of large field of view, low-cost and high-performance is the focus of current research and development. According to the aberration balance principle, the oblique incident reflective Schmidt correction plate equation was derived based on the normal incident Schmidt correction plate. For an optical system with the focal length of 1 700 mm, the imaging field angle of 4°, the operating wavelength of 0.4 μm to 0.9 μm, and the F number of 4.25, the Schmidt correction plate equation was solved and further optimized by using ZEMAX software as the initial structural parameter. The design results show that, the modulation transfer function (MTF) of this system is more than 0.35 at the Nyquist frequency of 100 lp/mm in the full field of view, and the distortion is less than 2.5 %, which indicates that the imaging quality is close to the diffraction limit. After the optimized design, the maximum deviation between Schmidt correction plate and near spherical surface is 0.005 mm, and the special compensator can complete the surface shape high-precision detection combined with the interferometer. The design of the Schmidt system can provide references for the development of astronomical telescopes with large field of view and wide spectrum.