The gallium nitride (GaN) light-emitting-diode (LED) top-bottom (or transmission-reflection) grating simulation results with error grating model are presented. The microstructure GaN bottom hole and top pillar gratings are calculated and compared with the non-grating (flat) case. Grating shapes simulated are either conical or cylindrical. A direct comparison of 181 different combined transmission-reflection grating cases using the finite difference time domain method is presented. The simulation results show that simple or direct combinations of the optimized top grating with the optimized bottom grating only produce a 42% light extraction improvement compared to the non-grating case, which is much lower than that of an optimized single grating case. This is due to the mismatch of grating parameters with the direct addition of the second grating structure, which changes the optical field distribution in the LEDs. Therefore, it is very important to optimize both top and bottom gratings simultaneously for the double-grating design. We also show the optimization of a double grating structure can achieve better performance than a single grating. Finally, transmission-reflection error gratings are also presented. It is also the first time to present randomization in GaN LED grating design and its effects in fabrication. Our data shows that the favorable light extraction improvement is at approximately 10-15% randomization. The randomization can achieve 230% improvement over the original grating at a randomization intensity factor of 12.8%.