The thermoresponsive drug-loaded hydrogels have attracted widespread interest in the field of medical applications due to their ease of delivery to structurally complex tissue defects. However, drug-resistant infections remain a challenge, which has prompted the development of new non-antibiotic hydrogels. To this end, we prepared chitosan-methacrylate (CTSMA)/gelatin (GEL) thermoresponsive hydrogels and added natural phenolic compounds, including tannic acid, gallic acid, and pyrogallol, to improve the efficacy of hydrogels. This hybrid hydrogel imparted initial crosslinking at physiological temperature, followed by photocuring to further provide a mechanically robust structure. Rheological analysis, tensile strength, antibacterial activity against E. coli, S. aureus, P. gingivalis, and S. mutans, and L929 cytotoxicity were evaluated. The experimental results showed that the hybrid hydrogel with CTSMA/GEL ratio of 5/1 and tannic acid additive had a promising gelation temperature of about 37 °C. The presence of phenolic compounds not only significantly (p < 0.05) enhanced cell viability, but also increased the tensile strength of CTSMA/GEL hybrid hydrogels. Moreover, the hydrogel containing tannic acid revealed potent antibacterial efficacy against four microorganisms. It was concluded that the hybrid hydrogel containing tannic acid could be a potential composite material for medical applications.