High-entropy alloy (HEA) nanoparticles are rising as promising catalysts but face challenges in both facile synthesis and correlation of the structure with properties. Herein, utilizing the highly reductive carbon-centered isopropyl alcohol radicals generated by UV irradiation, we report a simple yet robust wet chemical method to synthesize HEA nanoparticles under ambient conditions. These isopropanol radicals verified by electron paramagnetic resonance spectroscopy impose very large overpotentials to reduce diverse metal ions into HEA nanoparticles with five to seven different elements. Specially, the PtPdIrRhAuAgCu HEA nanoparticles on a reduced electrochemical graphene oxide (rEGO) support (PtPdIrRhAuAgCu-rEGO) demonstrate superior activity for the hydrogen evolution reaction (HER) across the entire pH range, with very small overpotentials of 11, 30, and 31 mV to deliver a current density of -10 mA cm-2 in 1 M KOH, 1 M phosphate buffer saline, and 0.5 M H2SO4, respectively. The excellent HER performance of PtPdIrRhAuAgCu-rEGO surpasses that of commercial Pt/C and most contemporary HER catalysts in the literature. Density functional theory calculations using random structures mimicking the chemical disordering in PtPdIrRhAuAgCu HEA confirm its superior HER activity and imply a possible correlation between HER activity and d-band centers of the nearest atoms in a face-centered cubic hollow site.