In this paper, we reviewed the current development and patents for the application of high-brightness and high-efficiency white light-emitting diode (LED). The high-efficiency GaN nanostructures, such as disk, pyramid, and rod were grown on LiAlO(2) substrate by plasma-assisted molecular-beam epitaxy, and a model was developed to demonstrate the growth of the GaN nanostructures. Based on the results, the GaN disk p-n junction was designed for the application of high brightness and high efficiency white LED.