Hydrogel adhesives are attractive for applications in intelligent soft materials and tissue engineering, but conventional hydrogels usually have poor adhesion. In this study, we designed a strategy to synthesize a novel adhesive with a thin hydrogel adhesive layer integrated on a tough substrate hydrogel. The adhesive layer with positive charges of ammonium groups on the polymer backbones strongly bonds to a wide range of nonporous materials' surfaces. The substrate layer with a dual hydrogen bond system consists of (i) weak hydrogen bonds between ,-dimethyl acrylamide (DMAA) and acrylic acid (AAc) units and (ii) strong multiple hydrogen bonds between 2-ureido-4[1H]-pyrimidinone (UPy) units. The dual hydrogen-bond network endowed the hydrogel adhesives with unique mechanical properties, e.g., toughness, highly stretchability, and insensitivity to notches. The hydrogel adhesion to four types of materials like glass, 316L stainless steel, aluminum, AlO ceramic, and two biological tissues including pig skin and pig kidney was investigated. The hydrogel bonds strongly to dry solid surfaces and wet tissue, which is promising for biomedical applications.