Stretchable displays that can change their shape and size under strain could be used to create displays with unconventional form factors. However, intrinsically stretchable light-emitting devices have poor luminous performance, such as low brightness. Here we show that intrinsically stretchable quantum dot light-emitting diodes (QLEDs) can be made using a mechanically soft and stretchable emissive layer consisting of a ternary nanocomposite of colloidal quantum dots, an elastomeric polymer and a charge transport polymer. The light-emitting layer maintains a nearly constant interparticle distance even under 50% strain, ensuring reliable operation of the QLED under stretching. The polymer-rich charge transport region at the bottom of the nanocomposite functions as a hole transport pathway to the embedded quantum dots. The QLEDs exhibit a turn-on voltage of 3.2 V and a maximum luminance of 15,170 cd m−2 at 6.2 V without loss of brightness, even when under 50% strain, and can be used to make stretchable full-colour passive-matrix QLED arrays.