Abstract: A catadioptric system uses a combination of lenses and mirrors placed in a carefully arranged configuration to capture a much wider field of view. However, images obtained by using a single-viewpoint catadioptric omnidirectional system have a large amount of visual distortion. To design a catadioptric omnidirectional system with undistorted imaging, appropriate surfaces were presented. The surfaces preserved a linear relationship between the angle of incidence of light onto the surface and the angle of reflection onto the imaging device, as does a normal mirror. The reflective mirror and the lens were designed for a catadioptric omnidirectional camera with the F number 3.3 and the field of view 138. The modulation transfer function is better than 0.6 at 66.7 lp/mm and the distortion is less than 4% over the whole active area of the image sensor. The deduction of the reflective surfaces offers an essential model and a computing method to design a catadioptric omnidirectional system with undistorted imaging.