The GaN-based blue light LED with double layer photonic crystals is designed to enhance the vertical light extraction efficiency. The effective index approximation method is proposed and used to solve the distribution of the modes in the LED model. The geometrical parameters including the depth of the top photonic crystal d, the thickness of the embedded photonic crystal T, and the distance between the active layer and the embedded photonic crystal D are optimized. Compared with other numerical optimization, the mode analysis used in this work can dramatically save computation time and reduce complexity. In addition, it can provide more theoretical details about the influence of these geometrical parameters on light extraction efficiency. It can be found that when the surface photonic crystal satisfies the condition of d / nPhCs, high order modes localized in the structure are still not cut off but the low order modes obtain less power since they are pushed away from the active layer. Hence, the light extraction efficiency reaches its maximum. The cap layer modes can be excited by the embedded photonic crystals, when this layer satisfies 100 nm T 300 nm and 100 nm D 200 nm, the cap layer modes gather much power from the active layer and interact with the surface photonic crystals more efficiently. Hence the light extraction efficiency is dramatically improved. With our optimized parameters, the light extraction efficiency can be achieved to be up 4 times that of ordinary LED. These results shows a significant promise of designing a high-efficiency GaN-based blue light LED.