Investigation in fabricating two-dimensional (2D) photonic crystal (PC) on sapphire substrates for enhancing external efficiency of GaN based light emitting diodes (LEDs) is presented. 2D-PC was fabricated on a sapphire substrate using holographic lithography and inductively coupled plasma (ICP) dry etching. LEDs with 2μm thick n-GaN layer，four pairs of InGaN/GaN quantum well structures and 200nm thick p-GaN layer were grown on the patterned sapphire substrate (PSS) by metal organic chemical vapor deposition (MOCVD). The PC fabricated on PSS has 2D hexagonal lattice pattern，with 3.8μm lattice constant and 800nm depth. LED output measurement shows 100% increase in the average luminous intensity of PSS-LEDs compared with that of conventioanl LEDs. The measured X-ray rocking curves of (0002) diffraction for GaN layers grown on patterned and non-patterned sapphire substrates indicate that the quality of GaN crystal grown on PSS is not improved，which implies that the large enhancement of external quantum efficiency of PSS-LED is not caused by the increase in internal efficiency but possibly by the increase in extraction efficiency，which results from the scattering of the PSS.