The production of the terpolymerpoly(3-hydroxybutyrate-co-3-hydroxyvalerate-co-4-hydroxybutyra te), P(3HB-eo-3HV-co-4HB), by Alcaligenes sp. A-04 was investigated to determine the superior biodegradable polymer properties over those of poly(3-hydroxybutyrate), P(3HB), and its copolymers. The highest terpolymer content of 68% (w/w) was produced by Alcaligenes sp. A-04 at 60 h by shake-flask cultivation. The terpolymer with 93 mol% 4HB mole fraction units was produced when the cultivation time was extended to 96 h. Moreover, it was found that Alcaligenes sp. A-04 could utilize 1,4-butanediol for the synthesis of 3HB and 4HB monomers as well as the sodium salt of 4-hydroxybutyrate. The terpolymer content was 30% (w/w) and the composition was P(33%3HB-co-16%3HV-co-51%4HB). Next, terpolymers with 4HB mole fraction units ranging from 50 to 90 mol% were produced by varying the medium composition and cultivation time. The thermal and mechanical properties of the resulting terpolymers were different from those of the copolymers with a similar mole fraction of monomer units. The terpolymer P(4%3HB-co-3%3HV-co-93%4HB) showed an elongation of 430%, a toughness of 33 MPa, and Young's modulus of 127 MPa similar to those of low-density polyethylene. The terpolymer P(11%3HB-co-34%3HV-co-55%4HB) showed Young's Modulus of 618 MPa similar to that of polypropylene.