Integral imaging is a promising 3D visualization technique for reconstructing 3D medical scenes to enhance medical analysis and diagnosis. However, the use of lens arrays inevitably introduces flipped images beyond the field of view, which cannot reproduce the correct parallax relation. To avoid the flipping effect in optical reconstruction, a twice-imaging lens array based integral display is presented. The proposed lens arrangement, which consists of a light-controlling lens array, a field lens array and an imaging lens array, allows the light rays from each elemental image only pass through its corresponding lens unit. The lens arrangement is optimized with geometrical optics method, and the proposed display system is experimentally demonstrated. A full-parallax 3D medical scene showing continuous viewpoint information without flipping is reconstructed in 45° field of view.