At present, the development and usage of degradable plastics instead of traditional plastics is an effective way to solve the pollution of marine microplastics. Poly (butylene adipate-co-terephthalate) (PBAT) is known as one of the most promising biodegradable materials. Nevertheless, the degradation rate of PBAT in water environment is slow. In this work, we successfully prepared four kinds of high molecular weight polyester copolyesters (PBATGA) via quaternary copolymerization. The results showed that the intrinsic viscosity of PBATGA copolymers ranged from 0.74 to 1.01 dL/g with a glycolic acid content of 0–40%. PBATGA copolymers had excellent flexibility and thermal stability. The tensile strength was 5~40 MPa, the elongation at break was greater than 460%, especially the elongation at break of PBATGA10 at 1235%, and the thermal decomposition temperature of PBATGA copolyesters was higher than 375 °C. It was found that PBATGA copolyester had a faster hydrolysis rate than PBAT, and the weight loss of PBATGA copolymers showed a tendency of pH = 12 > Lipase ≈ pH = 7 > pH = 2. The quaternary polymerization of PBAT will have the advantage of achieving industrialization, unlike the previous polymerization process. In addition, the polymerization of PBATGA copolyesters not only utilizes the by-products of the coal chemical industry, but also it can be promising in the production of biodegradable packaging to reduce marine plastic pollution.