Disclosed herein is a novel polymer having a structure based on a biodegradable polymer. In the novel polymer, the biodegradable polymer has at least one kind of functional groups from among a hydroxyl group and a carboxyl group, wherein the biodegradable polymer bears a functional group conjugated with a nitric oxide-releasing compound and a different functional group substituted with a photopolymerizable functional group, the nitric oxide-releasing compound comprising a NO donor. Also provided is a nanofiber fabricated from the modified biodegradable polymer. The nanofiber can be fabricated by electrospinning the novel polymer.