Designing hydrogel dressing with intrinsic antibacterial property to promote skin injury recovery remains a significant challenge. In this research, poly(aspartic hydrazide) with grafted betaine (PAHB) was designed and reacted with oxidized dextran (OD) to fabricate biodegradable PAHB/OD hydrogel and its application as wound dressing was systematically investigated. The PAHB/OD hydrogels exhibited fast gelation, strong tissue adhesion, preferable mechanical properties and biocompatibility. The grafted betaine endowed the hydrogel with antibacterial property and antibacterial rate enhanced through photothermal performance of composited CuS nanoparticles under near infrared (NIR) radiation. The CuS composited PAHB/OD hydrogel (CuS/hydrogel) with microporous morphology was used as burn wound dressing with loaded anti-inflammatory drug diclofenac sodium (DS) in mouse model. The results showed the DS loaded CuS/hydrogel (CuS@DS/hydrogel) promoted the tissue regeneration and suppressed the inflammatory response. The histological analysis and immunohistochemical expression confirmed the CuS@DS/hydrogel promote angiogenesis of the burn wound by regulating the expression of inflammatory cytokines (IL-6 and CD68) and vascular endothelial growth factor (VEGF). Overall, the CuS@DS/hydrogel hydrogel is a promising candidate as wound dressing due to its tissue adhesive, antioxidant, antibacterial and anti-inflammatory activities.