Based on the Diels–Alder reaction and hydroxyl-terminated polybutadiene (HTPB) binders of solid propellants, two novel compounds—furfuryl-terminated polybutadiene (FTPB) and trifurfuryl propane (TFP)—were designed and synthesized, and their structures were characterized. A new kind of reversible Diels–Alder reaction system was formed by FTPB as main resin, N,N′-1,3-phenylenedimaleimide (PDMI) as curing agent and TFP as chain extender. The results showed that this system had good mechanical properties with a tensile strength of 1.76 MPa and a tensile strain of 284% after curing, and the repair efficiency of the crack was 88%. Therefore, it could be used as a novel binder of energetic materials such as solid propellant and PBX explosives to provide them with self-repairing characteristics and improve the reliability for application.