Chronic wound infections caused by antibiotic-resistant bacteria have become a global health concern. This is attributed to the biofilm-forming ability of bacteria on wound surfaces, thus enabling their persistent growth. In most cases, it leads to morbidity and in severe cases mortality. Current conventional approaches used in the treatment of biofilm wounds are proving to be ineffective due to limitations such as the inability to penetrate the biofilm matrix; hence, biofilm-related wounds remain a challenge. Therefore, there is a need for more efficient alternate therapeutic interventions. Hydrogen peroxide (HP) is a known antibacterial/antibiofilm agent; however, prolonged delivery has been challenging due to its short half-life. In this study, we developed a hydrogel for the codelivery of HP and antimicrobial peptides (Ps) against bacteria, biofilms, and wound infection associated with biofilms. The hydrogel was prepared via the Michael addition technique, and the physiochemical properties were characterized. The safety, in vitro, and in vivo antibacterial/antibiofilm activity of the hydrogel was also investigated. Results showed that the hydrogel is biosafe. A greater antibacterial effect was observed with HP-loaded hydrogels (CS-HP; hydrogel loaded with HP and CS-HP-P; hydrogel loaded with HP and peptide) when compared to HP as seen in an approximately twofold and threefold decrease in minimum inhibitory concentration values against methicillin-resistant Staphylococcus aureus (MRSA) bacteria, respectively. Similarly, both the HP-releasing hydrogels showed enhanced antibiofilm activity in the in vivo study in mice models as seen in greater wound closure and enhanced wound healing in histomorphological analysis. Interestingly, the results revealed a synergistic antibacterial/antibiofilm effect between HP and P in both in vitro and in vivo studies. The successfully prepared HP-releasing hydrogels showed the potential to combat bacterial biofilm-related infections and enhance wound healing in mice models. These results suggest that the HP-releasing hydrogels may be a superior platform for eliminating bacterial biofilms without using antibiotics in the treatment of chronic MRSA wound infections, thus improving the quality of human health.