A guided bone regeneration membrane is a pivotal therapeutic modality used to maintain sufficient space for bone regeneration, which is of great significance in curing alveolar bone defects. Metformin has been found to possess the ability of promoting osteogenic differentiation of bone mesenchymal stem cells. To develop guided bone regeneration membranes with better osteoinductive ability, metformin was incorporated into polycaprolactone/chitosan nanofibrous membranes by electrospinning technique, followed by glutaraldehyde crosslinking to reinforce chitosan stability in aqueous solutions. The fabricated nanofibrous membranes were then characterized by scanning electron microscope, Fourier transform infrared spectroscopy, water contact angle testing, mechanical properties test, and drug release test. Furthermore, rats bone mesenchymal stem cells were seeded on membranes for the evaluation of the effect of metformin-loaded polycaprolactone/chitosan nanofibrous membranes on cell morphology, alkaline phosphate activity, and osteogenic mineralization in vitro. Our results showed that nanofibers were fabricated successfully with smooth surface free from beads formation. The crosslinked-polycaprolactone/chitosan/metformin membranes had a more appropriate water contact angle of 44.25 ± 1.37° and the drug release curve of metformin featured early sudden release and slow release in the later stage over a 23-day period. Besides, in vitro studies suggested that the crosslinked-polycaprolactone/chitosan/metformin membrane was more suitable for cell adhesion, proliferation, and osteogenic differentiation of bone mesenchymal stem cells. Consequently, the metformin-loaded polycaprolactone/chitosan nanofibrous membranes would be promoted for bone regeneration as guided bone regeneration membranes.