Green CdSe@ZnS quantum dots (QDs) of 9.5 nm size with a composition gradient shell are first prepared by a single-step synthetic approach, and then 12.7 nm CdSe@ZnS/ZnS QDs, the largest among ZnS-shelled visible-emitting QDs available to date, are obtained through the overcoating of an additional 1.6 nm thick ZnS shell. Two QDs of CdSe@ZnS and CdSe@ZnS/ZnS are incorporated into the solution-processed hybrid QD-based light-emitting diode (QLED) structure, where the QD emissive layer (EML) is sandwiched by poly(9-vinlycarbazole) and ZnO nanoparticles as hole and electron-transport layers, respectively. We find that the presence of an additional ZnS shell makes a profound impact on device performances such as luminance and efficiencies. Compared to CdSe@ZnS QD-based devices the efficiencies of CdSe@ZnS/ZnS QD-based devices are overwhelmingly higher, specifically showing unprecedented values of peak current efficiency of 46.4 cd/A and external quantum efficiency of 12.6%. Such excellent results are likely attributable to a unique structure in CdSe@ZnS/ZnS QDs with a relatively thick ZnS outer shell as well as a well-positioned intermediate alloyed shell, enabling the effective suppression of nonradiative energy transfer between closely packed EML QDs and Auger recombination at charged QDs.