Perovskite light-emitting diodes (LEDs) have attracted broad attention due to their rapidly increasing external quantum efficiencies (EQEs)1-15. However, most high EQEs of perovskite LEDs are reported at low current densities (<1 mA cm-2) and low brightness. Decrease in efficiency and rapid degradation at high brightness inhibit their practical applications. Here, we demonstrate perovskite LEDs with exceptional performance at high brightness, achieved by the introduction of a multifunctional molecule that simultaneously removes non-radiative regions in the perovskite films and suppresses luminescence quenching of perovskites at the interface with charge-transport layers. The resulting LEDs emit near-infrared light at 800 nm, show a peak EQE of 23.8% at 33 mA cm-2 and retain EQEs more than 10% at high current densities of up to 1,000 mA cm-2. In pulsed operation, they retain EQE of 16% at an ultrahigh current density of 4,000 mA cm-2, along with a high radiance of more than 3,200 W s-1 m-2. Notably, an operational half-lifetime of 32 h at an initial radiance of 107 W s-1 m-2 has been achieved, representing the best stability for perovskite LEDs having EQEs exceeding 20% at high brightness levels. The demonstration of efficient and stable perovskite LEDs at high brightness is an important step towards commercialization and opens up new opportunities beyond conventional LED technologies, such as perovskite electrically pumped lasers.