Building an angiogenesis microenvironment and inhibiting wound infection are of great significance for chronic wound repair. In this paper, polydopamine-encapsulated mesoporous bioglass (MBG@PDA) capsules were constructed to realize the integration of angiogenesis and infection inhibition through the formation of a composite hydrogel with modified hyaluronic acid (HAMA) to promote wound healing. The experiments showed that the composite hydrogel had good adhesion and toughness and promoted the migration of fibroblasts to accelerate the epithelialization process. In addition, in the composite hydrogel, MBG@PDA could release Mg2+ to promote the proliferation and migration of vascular endothelial cells for angiogenesis. At the same time, MBG@PDA in the composite hydrogel could facilitate the long-term release of drugs to inhibit the growth of Escherichia coli (E. coli) and Staphylococcus aureus (S. aureus) for reducing the possibility of wound infection. Finally, the results of in vivo experiments showed that a multifunctional dressing could repair wounds more quickly by promoting angiogenesis and reducing the pathological areas. In summary, the construction of these composite hydrogels can provide a repair method in the wound-repair field.