A facile method to fabricate three-dimensional branched ZnO/MgO nanowire heterostructures and their application as the efficient light-extraction layer in light-emitting diodes are reported. The branched MgO nanowires are produced on the hydrothermally-grown ZnO nanowires with a small tapering angle towards the tip (approximate to 6 degrees), by the oblique angle flux incidence of MgO. The structural evolution during the growth verifies the formation of the MgO nanoscale islands with strong (111) preferred orientation on very thin (5-7 nm) MgO (110) layer. The MgO nanobranches, then grown on the islands, are polycrystalline consisting of many grains oriented in specific directions of <200> and <220>, supported by the nucleation theory. The LEDs with the branched ZnO/MgO nanowire arrays show a remarkable enhancement in the light output power by 21% compared with that of LEDs with pristine ZnO nanowires. Theoretical calculations using a finite-difference time-domain method reveal that the nanostructure is very effective in breaking the wave-guiding mode inside the ZnO nanowires, extracting more light especially in radial direction through the MgO nanobranches.