Electrospun polymeric nanofibers have been extensively studied for biomedical materials because of their unique structures and relatively easy fabrication with biocompatible polymers. The amount of surface exposed amine groups increases as the blend ratio of block copolymer increases. Cell attachments on the nanofibers change according to the ratio of the block copolymer ((Poly(e-caprolactone, PCL), Poly(e-caprolactone)-Poly (ethylen glycol-$NH_2$)) in the blend. We assume that the PEG and amine moiety plays a significant role in biocompatibility of nanofiber surfaces. Collagen was used as a grafting material on the composite nanofibers to enhance the cell adhesion because the collagen is a major constituent of connective tissue.