Diabetic wounds are extremely difficult to heal due to the long duration and high recurrence rate. The bacterial infection caused by elevated blood glucose negatively affects the speed of wound healing. In this article, radially oriented nanofibers containing the natural antimicrobial agent purslane were prepared by electrostatic spinning. Subsequently, asiaticoside was loaded onto the surface of the fibers by electrostatic spraying. The experimental results indicated that radial nanofiber membranes exhibited uniform diameter distribution, suitable water vapor permeability, and good hydrophilicity as well as excellent antibacterial performance and biocompatibility. Due to the ordered arrangement, the radial nanofibers exhibited good wound healing ability, regular granulation tissue growth, and high collagen deposition. More importantly, the radially oriented fiber structure significantly promoted cell proliferation and adhesion. Based on these results, nanofiber membranes with a radially oriented structure have potential application prospects in the field of chronic diabetic wound healing.