Metal halide perovskite has emerged as a promising material for light-emitting diodes. In the past, the performance of devices has been improved mainly by optimizing the active and charge injection layers. However, the large refractive index difference among different materials limits the overall light extraction. Herein, we fabricate efficient methylammonium lead bromide light-emitting diodes on nanophotonic substrates with an optimal device external quantum efficiency of 17.5% which is around twice of the record for the planar device based on this material system. Furthermore, optical modelling shows that a high light extraction efficiency of 73.6% can be achieved as a result of a two-step light extraction process involving nanodome light couplers and nanowire optical antennas on the nanophotonic substrate. These results suggest that utilization of nanophotonic structures can be an effective approach to achieve high performance perovskite light-emitting diodes.