Solution-processable perovskites show highly emissive and good charge transport, making them attractive for low-cost light-emitting diodes (LEDs) with high energy conversion efficiencies. Despite recent advances in device efficiency, the stability of perovskite LEDs is still a major obstacle. Here, we demonstrate stable and bright perovskite LEDs with high energy conversion efficiencies by optimizing formamidinium lead iodide films. Our LEDs show an energy conversion efficiency of 10.7%, and an external quantum efficiency of 14.2% without outcoupling enhancement through controlling the concentration of the precursor solutions. The device shows low efficiency droop, i.e. 8.3% energy conversion efficiency and 14.0% external quantum efficiency at a current density of 300 mA cm , making the device more efficient than state-of-the-art organic and quantum-dot LEDs at high current densities. Furthermore, the half-lifetime of device with benzylamine treatment is 23.7 hr under a current density of 100 mA cm , comparable to the lifetime of near-infrared organic LEDs.