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The effect of gradual indium gallium nitride (InGaN) quantum wells (QWs) on the suppression of efficiency-droop in green light-emitting diodes (LEDs) is numerically investigated. The presented scheme increases the internal quantum efficiency by 45.5% at I=20 mA and 55.7% at I=100 mA, indicating a considerable reduction of efficiency-droop. This improvement is attributable mainly to the use of the gradual InGaN QW's structure that significantly alleviates band bending in the valence band, improving the transport efficiency of injected holes above that of conventional LEDs. The radiative recombination is thus enhanced as the overlap between electron and hole wave functions is increased. Most importantly, the leakage of injected electrons to p-type region is correspondingly reduced, in turn suppressing the efficiency-droop in the LED.