This paper demonstrates the strong enhancement of light extraction efficiency of light-emitting diodes (LEDs) by a novel three-dimensionally arranged micro-cavity. There are several optimal designed parameters, including chip dimensions, absorption coefficients, the shape of the micro-cavity and package are analyzed on the basis of a Monte-Carlo ray tracing simulation. The most important that studying includes GaN LEDs which are applied to various applications, including traffic signals, backlight system for LCD and outdoor illumination by white light LEDs. The functional of the three-dimensionally arranged micro-cavity is to make the light extraction from LED with high efficiency. The shape of micro-cavities are making like hexagon solids on the top view. The structure were evaluated and simulated by TracePro software respectively. The light extraction efficiency of LED can be greatly improved by three-dimensionally arranged micro-cavity. This study shows that the micro-cavities induced on the surface rather than that inside the LED greatly enhances the light extraction efficiency. This stipulation holds for both sapphire-based and Thin-GaN LEDs. The results indeed identify the attributes of the LED, which make it possible to achieve excellent luminance performance using a GaN-based approach from the LED of "three-dimensionally arranged micro-cavity". This structure was stringent expected to allow a high-efficiency LED, since the illumination systems needed for higher luminance energy can be added independently of the effects.