Lead-halide perovskites have been attracting attention for potential use in solid-state lighting. Following the footsteps of solar cells, the field of perovskite light-emitting diodes (PeLEDs) has been growing rapidly. Their application prospects in lighting, however, remain still uncertain due to a variety of shortcomings in device performance including their limited levels of luminous efficiency achievable thus far. Here we show high-efficiency PeLEDs based on colloidal perovskite nanocrystals (PeNCs) synthesized at room temperature possessing dominant first-order excitonic radiation (enabling a photoluminescence quantum yield of 71% in solid film), unlike in the case of bulk perovskites with slow electron-hole bimolecular radiative recombination (a second-order process). In these PeLEDs, by reaching charge balance in the recombination zone, we find that the Auger nonradiative recombination, with its significant role in emission quenching, is effectively suppressed in low driving current density range. In consequence, these devices reach a maximum external quantum efficiency of 12.9% and a power efficiency of 30.3 lm W-1 at luminance levels above 1000 cd m-2 as required for various applications. These findings suggest that, with feasible levels of device performance, the PeNCs hold great promise for their use in LED lighting and displays.