We present a grating model of two-dimensional (2D) rigorous coupled wave analysis (RCWA) to study top diffraction gratings on light-emitting diodes (LEDs). We compare the integrated-transmission of the non-grating, rectangular-grating, and triangular-grating cases for the same grating period of 6 \mum, and show that the triangular grating has the best performance. For the triangular grating with 6-\mm period, the LED achieves the highest light transmission at 6-m grating bottom width and 2.9-\mum grating depth. Compared with the non-grating case, the optimized light transmission improvement is about 74.6%. The simulation agrees with the experimental data of the thin polymer grating encapsulated flip-chip (FC) GaN-based LEDs for the light extraction improvement.