Widespread application of biodegradable polyesters is restrained by inferior mechanical properties, higher cost, and lack of reactive functional sites for further modification. A new class of multiblock copolymers bearing reactive sites on the main chains, composed of poly(butylene fumarate) (PBF) and poly(butylene succinate) (PBS), has been designed and synthesized to enhance the biodegradability of PBF and expand its application, while retaining the mechanical properties. The chemical structures of the copolymers were confirmed by H-1 NMR spectra and GPC. The two segments are compatible in both the amorphous and crystalline region, and form cocrystals because of their similar nature. The multiblock copolymers possess satisfactory thermal and mechanical properties. The degradation rate of copolymers is substantially accelerated by the copolymerization with PBS. The novel polymer may be directly used as biodegradable materials or be postfunctionalized to modify the physicochemical properties or to endow the polymers with special properties.