Poly(butylene furandicarboxylate)-b-poly(tetramethylene glycol) (PBF-PTMG) copolymers were synthesized from 2,5-furandicarboxylic acid (FDCA), 1,4-butanediol (BDO) and poly(tetramethylene glycol) (PTMG, theM_n is 1000 g/mol) through a process of esterification and polycondensation. The copolymers were characterized by ¹H NMR, GPC, DSC, POM, XRD, TGA and tensile strength measurements. The weight content of PTMG segments in the copolymers was 19.7%, 39.4% and 59.6% respectively, and their M_wranged from 59,300 to 85,900 g/mol. By combining the results of DSC, POM and XRD, they were block copolymers built up of crystallized PBF segments as the hard blocks and amorphous PBF and PTMG segments as the soft blocks, and the two segments were miscible in amorphous phase. As the content of PTMG segments increased, the glass transition temperature (T_g), the melting temperature (T_m), the crystallization temperature (T_c) and the crystallization ability of these copolymers decreased gradually, while their crystal structure changed little. For mechanical properties, the copolymers exhibited the characteristics of elastomers, showing good stress at break (16–26 MPa) and outstanding elongation at break (381–832%). The copolymers had greatly enhanced elasticity and flexibility properties as the content of PTMG segments increased, and the thermal annealing enhanced their tensile properties due to the more crystallinity and better regularity of PBF segments. Moreover, the TGA results revealed that PBF-PTMG copolymers had excellent thermal stability. Therefore, as novel bio-based copolymers, they might find applications in thermoplastics as well as elastomers.