We report the fabrication of efficient white light-emitting diodes (WLEDs) based on Cu : ZnInS/ZnS core/shell quantum dots (QDs) with super large Stokes shifts. The composition-controllable Cu : ZnInS/ZnS QDs with a tunable emission from deep red to green were prepared by a one-pot noninjection synthetic approach. The high performance Cu : ZnInS QD-WLEDs with the colour rendering index up to 96, luminous efficacy of 70-78 lm W(-1), and colour temperature of 3800-5760 K were successfully fabricated by integration of red and green Cu-doped QDs. Negligible energy transfer between Cu-doped QDs was clearly found by measuring the photoluminescence lifetimes of the QDs, consistent with the small spectral overlap between QD emission and absorption. The experimental results indicated low toxic Cu : ZnInS/ZnS QDs could be suitable for solid state lighting.