To meet the application demands of a wide field of view and fast focal ratio for an aerospace imaging spectrometer, a three-mirror folded Schmidt telescope using a freeform Offner convex grating spectrometer was designed to obtain a field of view 5°, focal ratio of 2, spectral range of 400-1 000 nm, and spectral resolution of 5 nm for a space hyperspectral imager. The expression of an axisymmetric anamorphic asphere Schmidt surface was given and calculated, and a manufacturing method was introduced. The optical system for a Schmidt spectrometer was designed and optimized using software Zemax. Results show that spectral distortion is less than 0.88%, the spectral smile is smaller than 1/3 pixel size, and the optical module transfer function is greater than 0.8. These imaging characteristics can meet the requirements of a space imager. The Schmidt system shows a simple configuration and uses only a single aspherical mirror. Because it possesses excellent imaging specifications, small distortion, small central obscuration, and a compact size, Schmidt is the best candidate for a space instrument with a large aperture, large field of view, and fast focal ratio.