We optimized the design of the flat encapsulant of a light-emitting diode (LED) package to obtain higher light output power (LOP), both by experiment and simulation using three-dimensional ray-tracing software. In the experiment, the refractive index of the encapsulant was varied (1.41 and 1.53). In addition, double-layer structures with these refractive indices (1.41/1.53) were investigated by varying the shape of the interface between the two among flat, concave, and convex. The experiments showed that the LOP of the double-layer encapsulant with convex interface increased by 13.4% compared to the single-layer encapsulant with a refractive index 1.41, which was explained by the increase of the light extraction efficiency (LEE) in connection with the increase of the critical angle (${ heta}_c$) and the decrease of the Fresnel reflection.