We　propose　a　simple　method　to　improve　the　light　extraction　in　GaN　based　light　emitting　diode.　Conventional　light　emitting　diode　has　an　extraction　limitation　due　to　the　totalinternal　reflection　which　occurs　at　the　interface　between　GaN　and　air.　By　using　periodic　grating　etched　at　the　GaN　layer,　we　can　couple　more　emitting　light　out　of　the　active　layer.　Tapering　the　grating　structure　would　facilitate　the　impedance　matching　between　GaN　light　emitting　diode　and　air,　which　can　enhance　broadband　light　extraction.　We　use　finite　difference　time　domain　method　to　numerically　find　the　best　tapering　grating　structure.　The　numerical　experiment　demonstrate　an　enhance　factor　4　of　our　proposed　structure　compared　with　the　conventional　one　over　broad　band　specctrum.　.　©　Maxwell　Scientific　Organization,　2013.