In order to achieve a desired irradiance distribution on target plane, we proposed an approach for the design of an asymmetrical TIR lens generating special facula in an area with a large height-diameter ratio, which can reach 1: 12. A mathematical model of a total internal reflection surface based on single LED chip and desired irradiance distribution of the target plane is established, by solving the equations, several 2-D curves are obtained, then combined these 2-D curves into asymmetrical surface by using modeling tools. The results show that this method can be used to produce different irradiance distribution, including polygon, ellipses, pentagram, heart-shaped and lots of different irregular shapes. In particular, the normal vector of luminous surface and target plane are equal, the contrast of boundary region can reach 10000:1 and its efficiency can reach more than 93%.