An innovative type of biodegradable thermoplastic elastomers with improved mechanical properties from very common and potentially renewable sources, poly(L-lactide)-b-poly(2-methyl-1,3-propylene glutarate)-b-poly(L-lactide) (PLA-b-PMPG-b-PLA)s, has been developed for the first time. PLA-b-PMPG-b-PLAs were synthesized by polycondensation of 2-methyl-1,3-propanediol and glutaric acid and successive ring-opening polymerization of L-lactide, where PMPG is an amorphous central block with low glass transition temperature and PLA is hard semicrystalline terminal blocks. The copolymers showed glass transition temperature at lower than −40 °C and melting temperature at 130–152 °C. The tensile tests of these copolymers were also performed to evaluate their mechanical properties. The degradation of the copolymers and PMPG by enzymes proteinase K and lipase PS were investigated. Microbial biodegradation in seawater was also performed at 27 °C. The triblock copolymers and PMPG homopolymer were found to show 9–15% biodegradation within 28 days, representing their relatively high biodegradability in seawater. The macromolecular structure of the triblock copolymers of PLA and PMPG can be controlled to tune their mechanical and biodegradation properties, demonstrating their potential use in various applications.