Bacterial infections and inflammation are two main factors for delayed wound healing. Coaxial electrospinning nanofibrous patches, by co-loading and sequential co-delivering of anti-bacterial and anti-inflammation agents, are promising wound dressing for accelerating wound healing. Herein, curcumin (Cur) was loaded into the polycaprolactone (PCL) core, and broad-spectrum antibacterial tetracycline hydrochloride (TH) was loaded into gelatin (GEL) shell to prepare PCL-Cur/GEL-TH core-shell nanofiber membranes. The fibers showed a clear co-axial structure and good water absorption capacity, hydrophilicity and mechanical properties. In vitro drug release results showed sequential release of Cur and TH, in which the coaxial mat showed good antioxidant activity by DPPH test and excellent antibacterial activity was demonstrated by a disk diffusion method. The coaxial mats showed superior biocompatibility toward human immortalized keratinocytes. This study indicates a coaxial nanofiber membrane combining anti-bacterial and anti-inflammation agents has great potential as a wound dressing for promoting wound repair.