A method for enhancing the light-extraction efficiency of GaInN light-emitting diodes (LEDs) by complete elimination of total internal reflection is reported. Analytical calculations show that GaInN LEDs with multilayer graded-refractive-index pillars, in which the thickness and refractive index of each layer are optimized, have no total internal reflection. This results in a remarkable improvement in light-extraction efficiency. GaInN LEDs with five-layer graded-refractive-index pillars, fabricated by cosputtering TiO2 and SiO2, show a light-output power enhanced by 73% and a strong side emission, consistent with analytical calculations and ray-tracing simulations.