Using photonic crystals (PCs), the extraction efficiency of the light-emitting diodes (LEDs) can be greatly enhanced by the effects of photonic band gap (PBG) and grating diffraction. The two theoretical methods are also discussed. Meanwhile, we demonstrate that LEDs can achieve high extraction efficiency by employing photonic crystal as diffraction grating. PCs with square lattice of cylindrical unit cells are fabricated in GaN layer of GaN-based blue LED. We present a theoretical discussion on the extraction efficiency of PC-LED, which relies on the effective medium theory and transmission matrix method to investigate the effect of lattice constant. The results show that the extraction efficiency of the high performance LEDs can achieve 61.8% when the lattice constant is 270 nm.