As the low luminous flux of one single LED, LED chip array plays important effect on achieving high luminous flux in all kinds of applied field, such as automotive lighting, street lighting, sensing and imaging, etc. However, LED chip array is an extended source rather than a point source of conventional one single LED. Obviously, lens design for LED chip array will be reconsider and redesign to accommodate this difference. In recent years, as the development of illumination optics, some excellent optical design methods for extended source have been improved and suggested. When the design method for point source is adopt to design the LED chip array with high flux and high uniformity, the obtained Lens is so huge that the advantage of small LED chip is dissipated at this condition. The supporting surface method is effective and commonly used. However, it is not convergent when solving the refractor problem of designing point light source near field. Based on the property of Cartesian oval, a modified method is proposed and the convergence of the modified method is verified by Monte-Carlo ray trace. The number of the Cartesian oval and the size of the lens can be firmly under control during the design, while generally the ratio between the sizes of the lens and the chip is greater than 5. Based on the modified supporting surface method, a compact lens design method for extended light source is constructed. And the LED illumination lens is designed by this method and fabricated, and the simulation result shows that this LED illumination lens can achieve uniform illumination at target surface.