It is an effective strategy to tailor material properties by copolymerization of monomers with different chemical structures and to adjust the compositions and sequence distributions of resultant copolymers. Although the biorenewable alpha-methylene-gamma-butyrolactone (MBL) as a comonomer has shown potential advantages to impart its copolymers with tunable properties and modifiable pendent vinyl groups, the copolymerization of MBL with other cyclic lactones to exclusively produce functional copolyesters with high MBL content remains as a big challenge mainly owing to the competing polymerization of highly stable five-membered gamma-butyrolactone ring and highly reactive exocyclic double bond. In this contribution, we presented the first organocatalytic ring-opening copolymerization (ROCP) of MBL with two cyclic lactones, i.e., epsilon-caprolactone (epsilon-CL) and delta-valerolactone (delta-VL), to produce exclusively functional copolyesters without formation of vinyl-addition P(MBL)(VAP) homopolymer. Copolyesters with MBL content in a wide range from similar to 6 to similar to 90 mol % were achieved by employing an organophosphazene base/urea binary catalytic system. The obtained copolyesters exhibited composition-dependent thermal properties, which have been carefully investigated herein.