In this paper, we have proposed a “Chess board” like photonic crystal (PhC) structure on top surface of layer in conventional LED, on top surface of n-GaN layer in vertical LED and an embedded PhC structure in n-GaN layer for achieving an improved light extraction in GaN/InGaN LEDs. The results are compared with that of the LED structures with conventional 2-D PhC structures and of the conventional LEDs. Results from these simulations show that the maximum light extraction for conventional LED having “Chess board” like structure occurs for a grating period of 0.6 with a grating-depth of 0.18 , which gives 4 times enhancement compared to that of conventional LED and 1.2–1.4 times compared to that of LED with conventional 2-D PhCs. In case of a vertical LED, the maximum enhancement in light extraction occurs for the same grating-period with a depth of 0.5 , which is 3.5 times compared to that of the conventional vertical LEDs. We have also simulated our proposed structure on top of -on-p-GaN layer in order to avoid the etching of p-GaN layer, which shows 2.2 times enhancement in comparison to that of conventional LED. For the proposed embedded PhC structure in n-GaN layer, the light extraction is enhanced by a factor of 2.8–3.5 as compared to the conventional LED.