Biodegradable plastic can decompose in the natural environment and thus effectively reduce the environmental pollution. Poly(butylene adipate-co-terephthalate) (PBAT) is a kind of polyester with good mechanical performance, degradability, and biocompatibility. In this study, a novel kind of poly(1,3-butylene adipate-co-1,4-butylene terephthalate) (PB′ABT) was synthesized with 1,3-butanediol, adipic acid, 1,4-butanediol and terephthalic acid as monomers through direct esterification and melt polycondensation to develop a kind of biodegradable polyester with more practical application value. A molecular weight of more than 50000 and intrinsic viscosity of 0.91-1.01 dL/g was achieved. The molecular structure of the polyester can be effectively adjusted with the monomer ratio, thereby affecting the properties, considering the thermal behavior, crystallinity, and mechanical performance increased with the 1,4-butadiene terephthalate (BT) unit content. Glass transition temperature (Tg), crystallization temperature (Tc), melting temperature (Tm) and crystallinity increased from -24.5 °C to 0 °C, 66.2 °C to 149.2 °C, 112.8 °C to 179.4 °C, and 20% to 33%, respectively. The highest tensile strength and elongation at break were 45 MPa and 1458%, respectively. PB′ABT-55 (molar ratio of BT: 55%) had higher thermal stability as compared with the biodegradable PBAT, and also superior tensile properties than the commercial PBAT. The results illustrated that the prepared PB′ABT is promising for wide application with good thermal stability, excellent tensile properties and biodegradability.