Abstract: Secondary optics are critical components of lighting emitting diode (LED) luminaries, which determine the optical efficiency and light distribution characteristics of luminaries. Based on Snell-s law, edge-ray principle, energy conservation principle and Etendue conservation principle, we investigated a design methodology using the numerical solutions of a set of first-order partial differential equations to obtain the X,Y coordinates of the total-internalreflection (TIR) compound surface. We established the corresponding relationship between the angle of LED emerging light and the coordinates of target points on the illumination plane. According to the corresponding relationship, we calculated the coordinates of the other points on the compound surface and fitted the points to the three-dimensional entity model by CAD. Then the three-dimensional entity model was imported into optical software to carry out the simulation. The results showed that a uniform rectangular facula on the road surface could be obtained by adopting TIR-compound secondary optical lens on LED.