A special illuminating system is proposed and designed in order to accurately test convex off-axis aspherical mirrors with computer-generated holograms (CGH). Illuminating system is used as reference system and used to project testing beam on under-testing aspherical mirrors vertically and also makes testing beam and reference beam near common-path. The geometrical system of this illuminating system is introduced and analysed. Then the relation of characters of work distance, focal length and the curvature radius of reference surface of illuminating system is obtained after simplify this multipurpose system to simple model system. The initial system can be realized by controlling these characteristic parameters as merit function during optical design process. Design results show that this method can satisfy requirement of system use.