Organometal halide perovskites can be processed from solutions at low temperatures to form crystalline direct-bandgap semiconductors with promising optoelectronic properties. However, the efficiency of their electroluminescence is limited by non-radiative recombination, which is associated with defects and leakage current due to incomplete surface coverage. Here we demonstrate a solution-processed perovskite light-emitting diode (LED) based on self-organized multiple quantum wells (MQWs) with excellent film morphologies. The MQW-based LED exhibits a very high external quantum efficiency of up to 11.7%, good stability and exceptional high-power performance with an energy conversion efficiency of 5.5% at a current density of 100 mAcm$^{-2}$. This outstanding performance arises because the lower bandgap regions that generate electroluminescence are effectively confined by perovskite MQWs with higher energy gaps, resulting in very efficient radiative decay. Surprisingly, there is no evidence that the large interfacial areas between different bandgap regions cause luminescence quenching.