Recently an optical diffusion of LED lamps has been studied actively. In this paper, the second lens applied to a cover of the LED lamp was analytically designed to having a wide angle distribution of light without diffuser characteristic by dispersing agent. In this process, We found a major factors that can help improve the performance of the lens. It is the refractive power of the lens, the Mie particle density of phosphor, and the arrangement of the LED. Through the final simulation, we can see the LED lamp is possible to get wide angle light distribution by proper source modeling and second lens designing. Also, we can see this simulated results are entirely consistent with measured data for light distribution. In this research, we present the shape of the second lens with wide angle distribution and derive the important factors for the second lens design.