An illumination system using LED sources for pocket-size projectors is designed. Its color gamut is much larger than the sRGB standard. The maximum theoretical efficiency of this system is 29.98% by non-imaging theory-based calculations. To analyze the system model, 1.5 x 10(6) rays are traced by using the LightTools software. The total light flux that illuminates the digital micromirror device is 44 lm and the American National Standards Institute 13-point uniformity on the surface is 91.55%, -91.15% with a system efficiency of 28.3%. The calculations are in good agreement with the simulation results. The illumination system can be used for personal pocket-size projectors providing a 15-20 in. (38-51 cm) color display with the brightness comparable with a laptop.