On the basis of the principle of integral imaging and the relation between camera array and display lens array, a pick-up system using a camera array for three-dimensional integral imaging was analyzed according to the geometric imaging theory and the ray tracing method, and the dependence of main recording parameters on display characteristics of integral imaging was obtained. A parameter design method for elemental images was proposed according to the display specifications and a pick-up system was designed by the proposed method in a pick-up distance of 49.6 cm and a camera space of 25 mm. The experimental results demonstrate that the pick-up system using the camera array can record the 3D information for a scene completely and the 3D display characteristics reach to the design requirements. Furthermore, the relationship between the pick-up parameters of the camera array and the display characters coincides with theoretical analysis, which verifies the display performance of designed system and the feasibility of the proposed method as well. The system can generate elemental images with large scenes and high resolution for mismatched full optical integral imaging systems.