Organic light-emitting diodes are emerging as leading technologies for both high quality display and lighting. However, the transparent conductive electrode used in the current organic light-emitting diode technologies increases the overall cost and has limited bendability for future flexible applications. Here we use single-layer graphene as an alternative flexible transparent conductor, yielding white organic light-emitting diodes with brightness and efficiency sufficient for general lighting. The performance improvement is attributed to the device structure, which allows direct hole injection from the single-layer graphene anode into the light-emitting layers, reducing carrier trapping induced efficiency roll-off. By employing a light out-coupling structure, phosphorescent green organic light-emitting diodes exhibit external quantum efficiency >60%, while phosphorescent white organic light-emitting diodes exhibit external quantum efficiency >45% at 10,000 cd m(-2) with colour rendering index of 85. The power efficiency of white organic light-emitting diodes reaches 80 lm W(-1) at 3,000 cd m(-2), comparable to the most efficient lighting technologies.