Highly power-efficient white organic light-emitting diodes (OLEDs) are still challenging to make for applications in high-quality displays and general lighting due to optical confinement and energy loss during electron-photon conversion. Here, an efficient white OLED structure is shown that combines deterministic aperiodic nanostructures for broadband quasi-omnidirectional light extraction and a multilayer energy cascade structure for energy-efficient photon generation. The external quantum efficiency and power efficiency are raised to 54.6% and 123.4 lm W-1 at 1000 cd m(-2). An extremely small roll-off in efficiency at high luminance is also obtained, yielding a striking value of 106.5 lm W-1 at 5000 cd m(-2). In addition to a substantial increase in efficiency, this device structure simultaneously offers the superiority of angular color stability over the visible wavelength range compared to conventional OLEDs. It is anticipated that these findings could open up new opportunities to promote white OLEDs for commercial applications.