Quantum dot (QD) light-emitting diodes (LEDs) are ideal for large-panel displays because of their excellent efficiency, colour purity, reliability and cost-effective fabrication1-4. Intensive efforts have produced red-, green- and blue-emitting QD-LEDs with efficiencies of 20.5 per cent4, 21.0 per cent5 and 19.8 per cent6, respectively, but it is still desirable to improve the operating stability of the devices and to replace their toxic cadmium composition with a more environmentally benign alternative. The performance of indium phosphide (InP)-based materials and devices has remained far behind those of their Cd-containing counterparts. Here we present a synthetic method of preparing a uniform InP core and a highly symmetrical core/shell QD with a quantum yield of approximately 100 per cent. In particular, we add hydrofluoric acid to etch out the oxidative InP core surface during the growth of the initial ZnSe shell and then we enable high-temperature ZnSe growth at 340 degrees Celsius. The engineered shell thickness suppresses energy transfer and Auger recombination in order to maintain high luminescence efficiency, and the initial surface ligand is replaced with a shorter one for better charge injection. The optimized InP/ZnSe/ZnS QD-LEDs showed a theoretical maximum external quantum efficiency of 21.4 per cent, a maximum brightness of 100,000 candelas per square metre and an extremely long lifetime of a million hours at 100 candelas per square metre, representing a performance comparable to that of state-of-the-art Cd-containing QD-LEDs. These as-prepared InP-based QD-LEDs could soon be usable in commercial displays.