The non-woven wound dressing with core–shell structured fibers was prepared by coaxial electrospinning. The polycaprolactone (PCL) was electrospun as the fiber’s core to provide mechanical strength whereas collagen was fabricated into the shell in order to utilize its good biocompatibility. Simultaneously, the silver nanoparticles (Ag-NPs) as anti-bacterial agent were loaded in the shell whereas the vitamin A palmitate (VA) as healing-promoting drug was encapsulated in the core. Resulting from the fiber’s core–shell structure, the VA released from the core and Ag-NPs present in the shell can endow the dressing both heal-promoting and anti-bacteria ability simultaneously, which can greatly enhance the dressing’s clinical therapeutic effect. The dressing can maintain high swelling ratio of 190% for 3 d indicating its potential application as wet dressing. Furthermore, the dressing’s anti-bacteria ability against Staphylococcus aureus was proved by in vitro anti-bacteria test. The in vitro drug release test showed the sustainable release of VA within 72 h, while the cell attachment showed L929 cells can well attach on the dressing indicating its good biocompatibility. In conclusion, the fabricated nanofibrous dressing possesses multiple functions to benefit wound healing and shows promising potential for clinical application.