A new concept of optical design with two-way multi-function for making full use of the lamp space was proposed.The rectangular composite paraboloid was constructed through combining the light emitting diode (LED) and the compound parabolic concentrator (CPC) based on the conservation of optical expansion and the principles of optical path reversibility and the edge ray.According to the latest performance requirements of reading and writing desk lamp in China, GB/T 9473-2017,the orthogonal experiment was designed based on three factors: the half width of light outlet, the irradiation height of desk lamp, and the length ratio of truncated cup body. It was determined that the most suitable rectangular compound parabolic parameters were as follows: the half width of light outlet of 50 mm, the max half angle of the inlet light of 47.73°, the truncated cup body length of 36 mm. Results show that in terms of illumination, the rectangular compound paraboloid satisfies the requirements for illumination and uniformity of national standard A and AA; in terms of low light collection, with the aid of the rectangular composite parabolic concentrator, the illumination of the solar chip position is 1.25 times higher than that without concentrator; in concentrating mode, the photovoltaic conversion efficiency of the solar chip is 1.66 times of that in non-concentrating mode. This is a complement to the current solar energy collection methods in the market, which are non-concentrated mode.