The possibilities of using gradient index (GRIN) lenses as the objective and relay lens in rigid endoscopic systems working in visible spectrum are investigated. The final aim of the project is to obtain a system providing diffraction limited image quality, which could be used for examining the gastrointestinal tract. This paper describes steps of the design of the system with working distance equal to 125 mm and angular field of view 25°. The diameter of the GRIN lenses is equal to 2,2 mm. Influence of the gradient of refractive index on the image quality is shown. Current results are analysed and future steps are described.