In recent years, three-dimensional (3D) display has received widespread attention. The light field display technology based on multi-layer translucent structures enables observers to directly acquire 3D scenes without wearing any auxiliary equipment, and has the advantages of high resolution and low cost. The use of liquid crystal panels as translucent structures makes it possible to realize dynamic 3D display. However, interactive 3D display can hardly be achieved due to the unacceptable long time to generate each frame of a 3D animation. In this paper, we reduce the time consumption for each frame by optimizing acquisition of the four-dimensional light field and calculation of the multi-layer LCD images. With the help of powerful rendering capabilities of OpenGL, we easily obtain the light field information of 3D scenes within less than 0.5s. The light field is rapidly decomposed into multiple LCD images utilizing parallel computing of graphics processing units. Human-computer interaction is realized through the development of Kinect. A 3D display system based on multi-layer LCDs is built, information flow between various components in the system is created, and interactive 3D display is implemented.