Lens for uniform illumination of rectangle area with LED light source was designed. Based on differential geometry, a series of partial non-linear equations were constructed. According to the conservation law of energy, energy mapping relations between the source and the target plane were constructed. The points of the surface were obtained by solving the equations with fourth order Runge-Kutta formulas, and the desired free-form surface was got by curve fitting with Rhinoceros software. With ray tracing in ASAP software, the result indicates that the optical efficiency is more than 94.01%, and the illumination uniformity of the predetermined illumination area on the target plane is better than 92.73%. The continuity of the free-form surface was also analyzed, and the result shows that the continuity of the freeform surface is determined by energy mapping relations.