Perovskite light-emitting diodes (PeLEDs) have shown excellent performance in the green and near-infrared spectral regions, with high color purity, efficiency, and brightness. In order to shift the emission wavelength to the blue, compositional engineering (anion mixing) and quantum-confinement engineering (reduced-dimensionality) have been employed. Unfortunately, LED emission profiles shift with increasing driving voltages due to either phase separation or the coexistence of multiple crystal domains. Here we report color-stable sky-blue PeLEDs achieved by enhancing the phase monodispersity of quasi-2D perovskite thin films. We selected cation combinations that modulate the crystallization and layer thickness distribution of the domains. The perovskite films show a record photoluminescence quantum yield of 88% at 477 nm. The corresponding PeLEDs exhibit stable sky-blue emission under high operation voltages. A maximum luminance of 2480 cd m-2 at 490 nm is achieved, fully one order of magnitude higher than the previous record for quasi-2D blue PeLEDs.