In order to satisfy the optical imaging system of ultraviolet (UV) focal plane arrays with wide spectrum and large field of view design demands, all-reflective Schmidt system was studied. Based on wavefront analysis at the center of curvature of a spherical mirror, the equations of refractive and reflective Schmidt correctors were derived. For avoiding central obscuration, the off-axis all-reflective Schmidt system was established which was characterized by the 240 nm~950 nm wide spectrum and ±5°field of view , the design results show that when λ=0.24 μm, u′m=5°, Δf≤0.031 5 mm, the detection is in the depth of focus and the image quality reaches the diffraction limit. The optical design method for Schmidt system can be applied to the UV imaging system with high resolution and wide spectrum.