In this study, a poly (octanediol citrate) (POC)/bioglass nanofiber composite was prepared by incorporating electrospun bioglass nanofiber (5, 10, and 15% w/w) into the POC matrix. The bioglass nanofiber interacted with POC via physical adsorption and carboxylate formation, and thus the addition of bioglass nanofiber increased the glass transition temperature, modulus and strength; however, decreased the elongation at break when the amount of bioglass nanofiber was up to 15% w/w. Compared to the pure POC elastomer, the POC/bioglass nanofiber composites exhibited accelerated stimulation to the mouse bone marrow mesenchymal stem cells (MSCs) on the cell growth and osteogenic differentiation. The level of alkaline phosphatase activity and cellular mineralization was higher for the POC/bioglass composites compared to the pure POC and increased with increasing amount of bioglass nanofiber within 14-day culture period. The gene expression of collagen type I and osteocalcin was also proportional to the bioglass nanofiber content of the composite. The results of this study showed that the composite of POC/bioglass nanofiber supported the osteogenic differentiation of MSCs and would be an excellent biomaterial candidate for applications in bone regeneration.