The epidermis of a deep burn wound is entirely absent and the dermal tissue sustains significant damage, accompanied by a substantial amount of tissue exudate. Due to the excessively humid environment, the formation of a scab on the wound becomes challenging, leaving it highly vulnerable to external bacterial invasion. In this work, a core−shell dual-drug-loaded nanofiber dressing was prepared by electrospinning technology for the synergistic treatment of a deep burn. The shell layer consists of polycaprolactone and chitosan encapsulating asiaticoside, with the core layer comprising the clathrate of 2hydroxypropyl-β-cyclodextrin and curcumin. Upon application to the wound, the dual-drug-loaded nanofiber dressing exhibited rapid release of asiaticoside, stimulating collagen deposition and promoting tissue repair. The core−shell structure and clathrate configuration ensured sustained release of curcumin, providing antibacterial and anti-inflammatory functions for the wound. The mechanical strength, broad-spectrum antibacterial ability, cell proliferation, and adhesion ability of the nanofiber dressing showed its potential as a medical dressing. This dressing also exhibited excellent wound healing promoting effects in the SD rat burn model. This paper provides a strategy for burn wound healing.