The property profiles of ABA triblock copolymers can be precisely customized by changing the chemical structure of the components. The identification of the midblock is the key point in the development of PLLA-containing ABA triblock copolymers. Two kinds of unsaturated aliphatic polyesters, crystalline poly(cis-butene succinate) (PcBS) and amorphous poly(cis-butene glutarate) (PcBG) with dihydroxyl end groups were prepared by polycondensation reactions. Then, dihydroxyl-terminated PcBS and PcBG were used as macroinitiators to initiate ring opening of polymerization of L-lactide toward two series of fully biobased biodegradable PLLA-b-PcBS-b-PLLA and PLLA-b-PcBG-b-PLLA triblock copolymers with PLLA as hard end-blocks. The influences of the midblocks and the endblocks length on microstructure, thermal and tensile properties of the triblock copolymers were studied. Compared to homopolymer PLLA, all the triblock copolymers had a much higher elongation at break with lower tensile strength and tensile modulus, depending on the length of PLLA blocks. It was found that the amorphous PcBG midblock plays a greater role than the crystalline PcBS midblock in enhancing the tensile toughness of ABA triblock copolymers. PLLA-b-PcBG-b-PLLA composed of shorter PLLA hard block displayed typical elastomeric behavior without yield, which is a promising aliphatic polyester-based thermoplastic elastomer. The unsaturated carbon-carbon double bonds in these polyesters backbone provide a variety of opportunities for further modifications.