A biocompatible small-diameter vascular graft, blood vessels conduit, or cell growth stimulator carrier composition which includes a completely biodegradable, hydrophilic non-gel material that has a controllable blood absorption or other biological liquid absorption ability, a controllable fiber architecture and pore sizes, and other biologically active properties, such as cell adhesion, proliferation and spreading, haemostatic and vascular tissue growth acceleration. The material retains its contour and shape when wet, and does not exhibit any swelling.