In this study, an alginate/PEG hydrogel was developed via a thiol-Michael addition reaction between oxidized quinone of catechols on dopamine-grafted sodium alginate (SA-DA) and sulfhydryl groups of 4-arm polyethylene glycol tetra-thiol (4-arm PEG-SH) under mildly basic conditions. Through the formation of thiol-terminated catechol groups, the accompanying oxidized catechols are reduced, significantly strengthening the internal network structure of the hydrogel and improving tissue adhesion. Meanwhile, the hydrogels have excellent self-healing properties due to the dynamic non-covalent bonds between the groups. Adjustment of hydrogel properties by varying the mass ratio of two hydrogel precursors. Due to the high content of thiol-terminated catechol groups, the Gel 3 exhibited good tissue adhesion, rapid self-healing ability, and other multifunctions beneficial to wound healing, including killing of E. coli and S. aureus, rapid hemostasis and promoting migration of L929 cells. The full-thickness skin wound model shows that the hydrogel dressing significantly accelerated wound contraction, with increased granulation tissue thickness, collagen disposition, and enhanced vascularization, thus promoting wound healing. Therefore, the thiol-Michael addition reaction is an effective method for creating multifunctional hydrogels, and the injectable self-healing alginate/PEG hydrogels prepared in this way could be used in the biomedical area as wound healing dressing materials.