We study the top transmission grating's improvement on GaN LED light extraction efficiency. We use the finite difference time domain (FDTD) method, a computational electromagnetic solution to Maxwell's equations, to measure light extraction efficiency improvements of the various grating structures. Also, since FDTD can freely define materials for any layer or shape, we choose three particular materials to represent our transmission grating: 1) non-lossy p-GaN, 2) lossy indium tin oxide (ITO), and 3) non-lossy ITO (α=0). We define a regular spacing between unit cells in a crystal lattice arrangement by employing the following three parameters: grating cell period (Α), grating cell height (d), and grating cell width (w). The conical grating model and the cylindrical grating model are studied. We also presented in the paper directly comparison with reflection grating results. Both studies show that the top grating has better performance, improving light extraction efficiency by 165%, compared to that of the bottom reflection grating (112%), and top-bottom grating (42%). We also find that when grating cells closely pack together, a transmission grating maximizes light extraction efficiency. This points our research towards a more closely packed structure, such as a 3-fold symmetric photonic crystal structure with triangular symmetry and also smaller feature sizes in the nano-scale, such as the wavelength of light at 460 nm, half-wavelengths, quarter wavelengths, etc.© (2011) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.