The main challenge encountered in clinical efficacy of tissue engineered vascular grafts is development of a biomimetic scaffold. To establish a scaffold resembling the architecture of the native blood vessels, a bilayered small-diameter nanofibrous tubular scaffold was fabricated by sequential electrospinning process. The inner layer of the scaffold was electrospun from a blend of fast degrading poly(glycerol sebacate) (PGS), a hydrophilic and elastomeric polymer, and slowly degrading polycaprolactone (PCL), with a weight ratio of 2:1, while the outer layer was electrospun using PCL. Our findings elucidated that nanofibrous PCL outer layer can improve the mechanical integrity and at the same time the presence of PGS within the nanofibers of the inner layer provides a nonthrombogenic interface. Additionally, electrospun PGS/PCL nanofibers with an appropriate balance between hydrophilic and hydrophobic characteristics served a suitable substrate for adhesion and proliferation of mesenchymal stem cells (MSCs); meanwhile, sufficient pore size provided by the inner layer facilitated cell infiltration into the interior of the scaffold.