Polyesters with free functional groups allow facile modifications with biomolecules, which can lead to versatile biomaterials that afford controlled interactions with cells and tissues. Efficient synthesis of functionalizable polyesters is still a challenge that greatly limits the availability and widespread applications of biofunctionalized synthetic polymers. Here we report a simple route to prepare a functionalizable polyester, poly(sebacoyl diglyceride) (PSeD) bearing free hydroxyl groups. The key synthetic step is an epoxide ring-opening polymerization, instead of the traditional polycondensation, that produces poly(glycerol sebacate) (PGS) [1]. PSeD has a more defined structure with mostly linear backbone, more free hydroxyl groups, higher molecular weight, and lower polydispersity than PGS. Crosslinking PSeD with sebacic acid yields a polymer five times tougher and more elastic than cured PGS. PSeD exhibits good cytocompatibility in vitro. Furthermore, functionalization by glycine proceeds with high efficiency. This versatile synthetic platform can offer a large family of biodegradable, functionalized polymers with tunable physiochemical and biological properties useful for a wide range of biomedical applications.