We describe a new biopolymer-based nanofibrous material possibly suitable for tissue engineering prepared by an environment-friendly organic solvent-free method. Glycogen, a biodegradable hyperbranched D-glucose polymer, comes from renewable resources and is normally present in man. It forms nanofibres by simple freeze-drying from aqueous solutions with concentration less than 0.5%. However, the architecture of the freeze-dried material depends on the starting biopolymer concentration within the tested range 0.1–5 wt%; in particular higher concentrations produce porous sponge-like structures with communicating pores. Because of the solubility of glycogen in water, nanofibres were modified by solvent-free grafting biodegradable poly(ethyl cyanoacrylate) from vapor phase. Exposing glycogen nanofibres to vapors of ethyl cyanoacrylate only slightly changed the material architecture while producing a water-insoluble biodegradable material with glycogen-to-poly(ethyl cyanoacrylate) ratio depending on the polymerization time. The material was proven to be hydrolytically degradable over the course of several months.