We report the preparation of a furan polymer, poly(2,5-furandimethylene succinate) by means of a condensation reaction between bio-based monomers. A reversible Diets Alder reaction between furan and maleimide groups allowed the formation of network polymers cross-linked by a bismaleimide. By controlling the amount of the bismaleimide, mechanical properties were varied widely. These network polymers healed well when their broken surfaces were activated by bismaleimide solutions or solvent. The polymers also displayed excellent self-healing ability without external stimulus. This polymer class offers a wide range of possibilities to produce materials from biomass that have both practical mechanical properties and healing ability. These materials have the potential to bring great benefits to our daily lives by enhancing the safety, performance, and lifetime of products.