Sustainability and high-performance of lightweight epoxy resin/carbon fiber composites are simultaneous challenges for future application in aerospace and wind power. The key to resolve them is designing epoxy resins from non-petroleum-based raw materials, recycling high-value carbon fibers, and improving interfacial interaction. We have increased availably interfacial interaction and performance by changing the topological structure of epoxy resins from linear to hyperbranched shape. The important molecular information about topological microstructure of hyperbranched polymers, such as hydrodynamic radius, mean square radii gyration, shape factor and relaxation rate, etc, are not still obtained to further disclose improving mechanism of interfacial strength. Here, the bio-based degradable hyperbranched epoxy resins (ETFP-n, n = 6, 12, 24) were firstly synthesized by biomass 2,5-furandicarboxylic acid. We have investigated systematically the topological properties of ETFP-n, including molecular size, degree of branching, hydrodynamic radius, mean square radii gyration, shape factor, interdiffusion coefficient, decay rate, conformation, et al, and highlighted the effects of topological structure and rheological property of ETFP-n on the mechanical and interfacial performance of the ETFP-n/carbon fiber composites, and discovered an interfacial improvement mechanism and an intact recycling mechanism of carbon fiber fabric. This work provides a promising approach for designing sustainable high-performance bio-based epoxy resin/carbon fiber composites.