Coaxial electrospinning is a new technique to fabricate continuous composite ultrafine fibers with core/shell structure, which has a broad application perspective in the biomedical field. In this study, ultrafine fibrous membranes of core/shell poly(vinyl pyrrolidone)/poly(L-lactide-co-epsilon-scaprolactone) (PVP/PLCL) were produced by coaxial electrospinning and the structural morphology of the obtained ultrafine fibers was observed by scanning electron microscopy and transmission electron microscopy. Electrospun PLCL and chitosan membranes were also prepared by traditional electrospinning as controls. The electrospun PVP/PLCL membranes showed the largest water absorption (501.3%) in phosphate buffer solution due to introduction of the PVP component and the core/shell fiber structure. Results of tensile tests indicated that the electrospun PVP/PLCL membranes possessed higher tensile strength and elongation-at-break, and lower Young's modulus than those of PLCL and chitosan membranes in both dry and wet states. Studies on cell adhesion, viability and morphology on the fibrous membranes showed that PVP/PLCL membranes could mimic the structure of natural extracellular matrices and positively promote cell-cell and cell-matrix interactions because of hydrophilicity/hydrophobicity balance.