Highly efficient organic light emitting diodes (OLEDs) based on multiple layers of vapor evaporated small molecules, indium tin oxide transparent electrode, and glass substrate have been extensively investigated and are being commercialized. The light extraction from the exciton radiative decay is limited to less than 30% due to plasmonic quenching on the metallic cathode and the waveguide in the multi-layer sandwich structure. Here we report a flexible nanocomposite electrode comprising single-walled carbon nanotubes and silver nanowires stacked and embedded in the surface of a polymer substrate. Nanoparticles of barium strontium titanate are dispersed within the substrate to enhance light extraction efficiency. Green polymer OLED (PLEDs) fabricated on the nanocomposite electrode exhibit a maximum current efficiency of 118 cd/A at 10,000 cd/m(2) with the calculated external quantum efficiency being 38.9%. The efficiencies of white PLEDs are 46.7 cd/A and 30.5%, respectively. The devices can be bent to 3 mm radius repeatedly without significant loss of electroluminescent performance. The nanocomposite electrode could pave the way to high-efficiency flexible OLEDs with simplified device structure and low fabrication cost.