The development of hydrogel wound dressings that facilitate rapid healing is a complex task, primarily due to the necessity of integrating multiple functional attributes, including air permeability, adhesion, antibacterial efficacy, and biocompatibility. In this study, we employed fatty acid-modified carboxymethyl chitosan (CMCS) to fabricate a multifunctional antibacterial hydrogel dressing. This dressing exhibits adjustable hydrophobicity, robust mechanical properties, and potent antibacterial activity, with polyacrylamide (PAM) and tannic acid (TA) serving as the primary constituents. The study demonstrated that the incorporation of hydrophobic structures significantly enhanced the tensile strength, compressive properties, and adhesive capacity of hydrogels. In addition, the release curve of TA showed that fatty acids played a vital role in enhancing the antibacterial properties of hydrogels, which may increase the release of TA. Furthermore, the length of the carbon chain has a significant effect on the mechanical properties and hydrophobic properties of the hydrogel. In summary, the TA/(C14-g-CMCS)/PAM hydrogel has excellent antibacterial properties, which can effectively prevent bleeding, accelerate wound closure, and promote tissue regeneration. Therefore, the TA/(FA-g-CMCS)/PAM hydrogel with adjustable hydrophobicity is expected to be the best candidate for accelerating wound healing and promoting rapid regeneration of skin tissue.