A pico-projector is a compact and mobile projector that has an infinite focus. We apply the pico-projector to a projection-type integral imaging system, which can expand the image depth to form multiple central depth planes. In a projection-type integral imaging system, the image flipping problem arises because the expanded elemental images pass through a lens array. To solve this problem, we propose the ray tracing of a pico-projector at a central depth plane and compensate the elemental image using a pixel-mapping process. Experiments to verify the proposed method are performed, and the results are presented.