Monolithic three-dimensional integration technology can eliminate the need for mechanical alignment between driving circuits and light-emitting diode (LED) pixels, leading to ultrahigh-resolution displays. However, this is challenging for red micro-LEDs, which are typically based on AlGaInP/GaInP, because of their low quantum efficiency and performance degradation when the pixel size is reduced. Here we report a high-pixel-density (1,700 pixels per inch) red active-matrix display consisting of micro-LEDs based on an epitaxial AlInP/GaInP double-quantum-well structure and silicon complementary metal-oxide-semiconductor integrated circuits. The epitaxial layer exhibits high internal quantum efficiency at low current densities (less than 10 A cm-2) due to a hole-dominant quantum well that reduces the non-radiative Shockley-Read-Hall recombination caused by electron lateral diffusion. We also use thickness fluctuation scattering in the quantum well to minimize the size-dependent quantum efficiency shift to higher current densities when reducing the size of the red micro-LEDs.