This work developed biodegradable nanofibrous drug-eluting membranes that provided sustained release of metformin for repairing wounds associated with diabetes. To prepare the biodegradable membranes, poly-d-l-lactide-glycolide (PLGA) and metformin were first dissolved in 1,1,1,3,3,3-hexafluoro-2-propanol (HFIP) and were spun into nanofibrous membranes by electrospinning. An elution method and an HPLC assay were utilized to characterize the in vivo and in vitro release rates of the pharmaceuticals from the membranes. The biodegradable nanofibrous membranes released high concentrations of metformin for more than three weeks. Moreover, nanofibrous metformin-eluting PLGA membranes were more hydrophilic and had a greater water-containing capacity than virgin PLGA fibers. The membranes also improved wound healing and re-epithelialization in diabetic rats relative to the control. The experimental results in this work suggest that nanofibrous metformin-eluting membranes were functionally active in the treatment of diabetic wounds and very effective as accelerators in the early stage of healing of such wounds.