Infected wounds are difficult to heal because they are vulnerable to bacterial attacks, inflammatory responses, and oxidative stress. To promote the healing of infected wounds, we developed an injectable dual-network hydrogel TFAEP (TA-Fe, APS, EPL-GMA, PVA) based on ε-poly-l-lysine-graft-glycidyl methacrylate (EPL-GMA), polyvinyl alcohol (PVA), and tannic acid-iron (TA-Fe). TA-Fe formed a stable redox pair, which acted as a dual-autocatalytic system to activate ammonium persulfate, generate free radicals, and subsequently induce EPL-GMA polymerization. Then PVA formed hydrogen bonds with TA molecules. Here, TA-Fe not only simulated peroxidase to convert H2O2 into hydroxyl radicals (OH), but also exhibited good near-infrared photothermal conversion efficiency, which all endowed the hydrogel with excellent antibacterial ability. In addition, the hydrogel could remove excessive reactive oxygen species and reactive nitrogen species, alleviating oxidative stress and reducing inflammation response due to the presence of TA molecules. Moreover, the hydrogel showed good injectability and tissue adhesion, ensuring the close adhesion of the hydrogel to the wound and achieving the maximum function. In vivo experiments demonstrated that the hydrogel promoted infected wound healing by accelerating epidermal regeneration, promoting angiogenesis and collagen deposition, and facilitating the expression of anti-inflammatory factors.