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The ordinary ring-remote-phosphor structure consisting of an inverted-cone-lens encapsulant and a surrounding ring-remote-phosphor layer reduces the probability of the backward light from the phosphor layer to the absorptive light-emitting diode (LED) chip and then increases the package extraction efficiency. However, some of the blue light emitting from the LED chip impinges on the inverted-cone-lens surface and then escapes without hitting the ring-remote-phosphor layer. The blue light leakage from the inverted-cone-lens surface is a serious problem for the ring-remote-phosphor structure devices in use, because it will lower the actual illumination effects and result in discomfort for the eyes. In this paper, we discuss the predominant factors of the blue light leakage from the inverted-cone-lens surface and propose an improve ring-remote-phosphor structure that utilizes an inverted-cone-lens encapsulant with gradient surface to decrease the blue light leakage. Ray-tracing simulations are performed to analyze the blue light leakages from the ordinary and improved inverted-cone-lens encapsulants in the ring-remote-phosphor structures. The simulation results show that the improved inverted-cone-lens encapsulants get almost no blue light leakage from the inverted-cone-lens surface directly and then lessen the discomfort for the eyes. Our results further demonstrate that the improved ring-remote-phosphor structure device will have higher angular color uniformity than the ordinary one.