The ever-shrinking electrostatic capacitor with its high dielectric permittivity and ferroelectric polarization can store large quantities of electrical charge and energy for compact electronics and electrical power systems, leading to applications including volatile/nonvolatile high-storage-density memories and energy-efficient complementary metal-oxide-semiconductor (CMOS) devices. Innovative use of CMOS-compatible HfO2-based materials with high permittivities of 27–52 and polarizations of 17–50 μC/cm2 could foster their integration into few-nanometre-scale devices. Here we report giant remanent polarization of 331 μC/cm2 for a 0.3-μm-sized Hf0.5Zr0.5O2 thin-film capacitor, combined with ultrahigh linear permittivity of ≥921, stored charge density of 295 μC/cm2 and energy density of 566 J/cm3 within a 4.4-μm-sized capacitor when the material’s ferroelectricity disappears suddenly after polarization fatigue, much better than relaxor ferroelectric thin films (133–152 J/cm3). The giant polarization originates from formation of high-density Zr-rich polar clusters near the edge region of the Hf0.5Zr0.5O2 thin-film capacitor after plasma treatment and remains unchanged at low temperatures. This enables high-density integration of extremely scaled logic and memory devices for low-voltage operation.