This study investigated a graded-refractive-index (GRIN) coating pattern capable of improving the light extraction efficiency of GaN light-emitting diodes (LEDs). The planar LEDs had total internal reflection thanks to the large difference in refractive index between the LED semiconductor and the surrounding medium (air). The main goal of this paper was to reduce the trapped light inside the LED by controlling the refractive index using various compositions of (TiO2)x(SiO2)1−x in GRIN LEDs consisting of five dielectric layers. Several types of multilayer LEDs were simulated and it was determined the transmittance value of the LEDs with many layers was greater than the LEDs with less layers. Then, the specific ranges of incident angles of the individual layers which depend on the refractive index were evaluated. According to theoretical calculations, the light extraction efficiency (LEE) of the five-layer GRIN is 25.29 %, 28.54 % and 30.22 %, respectively. Consequently, the five-layer GRIN LEDs patterned enhancement outcome LEE over the reference planar LEDs. The results suggest the increased light extraction efficiency is related to the loss of Fresnel transmission and the release of the light mode trapped inside the LED chip by the graded-refractive-index.