In order to enhance the light-emitting diode (LED) light extraction efficiency, the influences of grating shapes (rectangle, isosceles trapezoid and isosceles triangle) on the extraction efficiency are analyzed. The LED integrated with different shaped gratings is optimized based on the equivalent medium theory and the rigorous coupled-wave analysis method. The light extraction efficiencies for three LEDs with different optimal structures are simulated by the finite difference time domain method. The research results show that, when the wavelength is within the range of 0.4-0.5 μm, the light extraction efficiency of a flip-chip LED with an isosceles triangle shaped grating is larger than 70%, and the maximum is up to 77.75%, while that of a flip-chip LED with a trapezoid shaped grating is the lowest and its maximum is only 58%.