Electrospun chitosan (CTS) nanofibers have been well known for use as a wound dressing in the biomedical field. Nevertheless, fatal bacterial infections are still a serious problem when CTS nanofibers are used for wound treatment. In this study, we designed a novel wound dressing based on blending the chitosan with polyurethane (CTS/PU) containing silver sulfadiazine (AgSD) in order to enhance both antibacterial activity and mechanical strength. This fiber sheet was produced using the electrospinning (ELSP) technique. The CTS/PU containing AgSD fiber sheet was characterized by energy-dispersive X-ray spectroscopy (EDX). The physicochemical properties of the CTS/PU/AgSD fiber sheets were also characterized by thermogravimetric analysis (TGA) and Fourier transform infrared spectroscopy (FT-IR). The electrospun fibers were morphologically characterized by scanning electron microscopy (SEM) and transmission electron microscopy (TEM). For an in vitro evaluation, the CTS/PU/AgSD fiber sheets were tested for their antibacterial activity against gram-negative Pseudomonas aeruginosa (P. aeruginosa), gram-positive Staphylococcus aureus (S. aureus) and Methicillin-resistant Staphylococcus aureus (MRSA). The results indicate that CTS/PU/AgSD fiber sheets have strong antimicrobial activity as displayed by inhibition of bacterial growth and prevention of infection during the healing process. These results indicate that this material would be good for use as a wound dressing material.