Light Emitting Diode (LED) technology is very common in everyday life. Due to the large refractive index difference between LED material and air, many excited photons from the active layer cannot be passed on to the air, thereby Total Internal Reflection (TIR) will occur and reducing the Light Extraction Efficiency (LEE) of LED. The use of nanopatterns on the LED surface can help trapped photons to get out of the LED by changing the direction and angle of photons’ propagation. Because the shape of the nanopattern will affect the increase in the LEE of LEDs and its fabrication is expensive, simulations are needed to design and study the effect of the shape and size of the nanopattern on the LEE of LEDs. In this study, FDTD simulations will be carried out on nano-sized grating patterns on the ZnS:Cu LED surface and then compared with experimental results to see the accuracy of the simulation results using Ansys Lumerical FDTD. The simulation results obtained in light emission distribution are consistent with the real measurement results. The simulation results are also used to evaluate the performance of the LEDs with and without the nanopattern on the surface.