The aim of this study was to develop novel biomedical electrospun nanofiber mats for controlled drug release, in particular to release a drug directly to an injury site to accelerate wound healing. Here, nanofibers of chitosan (CS), poly(ethylene oxide) (PEO), and a 90 : 10 composite blend, loaded with a fluoroquinolone antibiotic, such as ciprofloxacin hydrochloride (CipHCl) or moxifloxacin hydrochloride (Moxi), were successfully prepared by an electrospinning technique. The morphology of the electrospun nanofibers was investigated by scanning electron microscopy. The functional groups of the electrospun nanofibers before and after crosslinking were characterized by Fourier transform infrared spectroscopy. X-ray diffraction results indicated an amorphous distribution of the drug inside the nanofiber blend. In vitro drug-release evaluations showed that the crosslinking could control the rate and period of drug release in wound-healing applications. The inhibition of bacterial growth for both Escherichia coli and Staphylococcus aureus were achieved on the CipHCl-and Moxi-loaded nanofibers. In addition, both types of CS/PEO and drug-containing CS/PEO nanofibers showed excellent cytocompatibility in the cytotoxicity assays.