Flexible organic light-emitting diodes are gaining increasing importance as a leading technology for high-quality displays and lighting in wearable electronics due to their low power consumption, excellent color gamut, and the desirable mechanical flexibility with soft materials and curvilinear surfaces. However, further enhancements in efficiency are still challenging because of the optical confinement and limited light out-coupling efficiency. Here, a simple and wavelength-independent light extraction scheme is demonstrated using the biomimetic quasirandom nanostructures that can simultaneously enhance the out-coupling of the waveguided light and allow the minimized ohmic losses without spectral distortion. Compared to periodic grating structures, the nanoimprinted quasirandom nanostructures can broaden the periodicity and randomize the emission directionality, leading to the superiority of color stability over the visible wavelength range for a large variation of viewing angles. The resulting external quantum efficiency and current efficiency are 1.51 and 1.43 times that of a conventional flexible organic light-emitting diode used as a comparison, respectively.