Adhesives with robust but readily detachable wet tissue adhesion are of great significance for wound closure. Polyelectrolyte complex adhesive (PECA) is an important wet tissue adhesive. However, its relatively weak cohesive and adhesive strength cannot satisfy clinical applications. Herein, modified tannic acid (mTA) with a catechol group, a long alkyl hydrophobic chain, and a phenyl group was prepared first, and then, it was mixed with acrylic acid (AA) and polyethylenimine (PEI), followed by UV photopolymerization to make a wet tissue adhesive hydrogel with tough cohesion and adhesion strength. The hydrogel has a strong wet tissue interfacial toughness of ∼1552 J/m, good mechanical properties (∼7220 kPa cohesive strength, ∼873% strain, and ∼33,370 kJ/m toughness), and a bursting pressure of ∼1575 mmHg on wet porcine skin. The hydrogel can realize quick and effective adhesion to various wet biological tissues including porcine skin, liver, kidney, and heart and can be changed easily with triggering urea solution to avoid tissue damage or uncomfortable pain to the patient. This biosafe adhesive hydrogel is very promising for wound closure and may provide new ideas for the design of robust wet tissue adhesives.