To improve light extraction efficiency (LEE) of the GaN-based LEDs, it has become a practical technique to form 2D periodic micro/nanostructure arrays in an n- or p-GaN layer. However, the fabrication of micro/nanostructure arrays in the thinner p-GaN layer can deteriorate the electrical characteristics, sometimes even damage the QWs active region. In this study, numerical simulations based on the Monte Carlo ray tracing method were carried out to investigate the influence of the different periodic arrays in the thicker n-GaN layer on the LEE of the LEDs. To find the optimal structure, the study was divided into three parts. Firstly, the parametrical influence of the different periodic arrays on the LEE was numerically simulated. The results showed that micro-cone arrays can effectively enhance the LEE and the maximum LEE can be obtained as the bottom of each cone pattern was in contact with adjacent cones. Secondly, by comparing micro-cone arrays with micro-pyramid arrays, the micro-cone arrays were superior to micro-pyramid arrays in terms of enhancing LEE. Lastly, the truncated cone arrays and truncated cone hole arrays with different upper radius were studied. The results indicated that the truncated cone arrays in top radius of less than 0.4µm showed a certain enhancement of the LEE and about 3 times LEE improvement was obtained as Rtop=0.2μm and h=1.0μm, compared with the planar flip-chip LEDs. Our results will provide important theoretical implications in development of high-power and high-brightness LEDs.