The purpose of this work is to develop a novel ultrathin fibrous membrane with a core-sheath structure as antibacterial food packaging film. Coaxial electrospinning was exploited to create the core-sheath structure, by which the delivery regulation of the active substance was achieved. Resveratrol (RE) and silver nanoparticles (AgNPs) were loaded into electrospun zein/polyethylene oxide ultrathin fibers to ensure a synergistic antibacterial performance. Under the assessments of a scanning electron microscope and transmission electron microscope, the ultrathin fiber was demonstrated to have a fine linear morphology, smooth surface and obvious core-sheath structure. X-ray diffraction and Fourier transform infrared analyses showed that RE and AgNPs coexisted in the ultrathin fibers and had good compatibility with the polymeric matrices. The water contact angle experiments were conducted to evaluate the hydrophilicity and hygroscopicity of the fibers. In vitro dissolution tests revealed that RE was released in a sustained manner. In the antibacterial experiments against Staphylococcus aureus and Escherichia coli, the diameters of the inhibition zone of the fiber were 8.89 ± 0.09 mm and 7.26 ± 0.10 mm, respectively. Finally, cherry tomatoes were selected as the packaging object and packed with fiber films. In a practical application, the fiber films effectively reduced the bacteria and decreased the quality loss of cherry tomatoes, thereby prolonging the fresh-keeping period of cherry tomatoes to 12 days. Following the protocols reported here, many new food packaging films can be similarly developed in the future.