We report on mechanically strong, water-insoluble hydrogen-bonded nanofiber mats composed of a hydrophilic polymer and a natural polyphenol that exhibit prolonged antioxidant activity. The high performance of fibrous mats resulted from the formation of a network of hydrogen bonds between a low-molecular-weight polyphenol (tannic acid, TA) and a water-soluble polymer (polyvinylpyrrolidone, PVP) and could be precisely controlled by the TA-to-PVP ratio. Dramatic enhancement (5- to 10-fold) in tensile strength, toughness, and Young’s moduli of the PVP/TA fiber mats (as compared to those of pristine PVP fibers) was achieved at the maximum density of hydrogen bonds, which occurred at ∼0.2–0.4 molar fractions of TA. The formation of hydrogen bonds was confirmed by an increase in the glass-transition temperature of the polymer after binding with TA. When exposed to water, the fibers exhibited composition- and pH-dependent stabilities, with the TA-enriched fibers fully preserving their integrity in acidic and neutral media. Importantly, the fiber mats exhibited strong antioxidant activity with dual (burst and prolonged) activity profiles, which could be controlled via fiber composition, a feature useful for controlling radical-scavenging rates in environmental and biological applications.