Techniques using biomass-based materials have become important to reduce the impacts of global warming and the depletion of petroleum resources. Changing biomass from edible to inedible is essential to solve global food issues. Furan derivatives are ideal chemicals for green chemistry because they are produced from inedible biomass resources. Here, we report the preparation of a biomass-based oxabicyclic dicarboxylic anhydride derived from furan derivatives and its polymerization with several α,ω-diols to polyoxabicyclates. ¹H NMR spectra and MALDI-TOF MS measurements verified the chemical structure of the polyoxabicyclates. Polyoxabicyclates prepared using 1,3-propanediol or 1,4-butanediol could be moulded into elastic films by melt pressing. Tensile strength testing of the films indicated that they were highly elastic. Furthermore, the films had good transparency in the visible region.