Using finite-difference time-domain （FDTD） method, we found the relationship between filling factor and band gap of square and hexagonal array of circular photonic crystal, and obtained the geometric parameters of the 2D photonic crystal, for which the number of bandgaps are the greater. Using FDTD method to calculate the extraction efficiency of the photonic crystals with the parameters, we verified the enhancement in extraction efficency of the GaN-based blue light-emitting diode based on the square and hexagonal array of circular photonic crystals with the the parameters, and the hexagonal arrangement is better than the square arrangement. By using the bang gap theory and equivalent medium theory was analyzed the mechanism of antireflection.