To improve the internal quantum efficiency of green light-emitting diodes, we present the numerical design and analysis of bandgap-engineered W-shaped quantum well. The numerical results suggest significant improvement in the internal quantum efficiency of the proposed W-LED. The improvement is associated with significantly improved hole confinement due to the localization of indium in the active region, leading to improved radiative recombination rate. In addition, the proposed device shows reduced defect-assisted Shockley-Read-Hall (SRH) recombination rate as well as Auger recombination rate. Moreover, the efficiency rolloff in the proposed device is associated with increased built-in electromechanical field.