There is herein described a LED lighting device utilizing quantum dots in layers on top of an LED chip. The quantum dots layers and the LED chip are arranged with gradient refractive indices, so that the refractive index of each layer is preferably less than the refractive index of the immediately underlying layer or chip. The quantum dots with emission peaks at longer wavelengths are preferably arranged in lower layers closer to the LED chip; while the quantum dots with emission peaks at shorter wavelengths are arranged in higher layers farther from the LED chip.