The present invention relates to a biodegradable copolyester of high molecular weight and narrow molecular weight distribution. The copolyester has a M.sub.w of 100,000-600,000 g/mol, and a molecular weight distribution of 1.2-3. The process for synthesizing the polyester comprises the steps of: 1) adding the following monomers and an optional catalyst component Cat1 to carry out interesterification and/or esterification: (a) aromatic dicarboxylic acid, ester thereof, anhydride thereof, or mixture thereof, (b) aliphatic diol, alicyclic diol or mixture thereof, and (c) aliphatic dicarboxylic acid, alicyclic dicarboxylic acid, ester thereof, anhydrides thereof, or a mixture thereof; 2) prepolymerizing the reaction system under vacuum; and adding a catalyst component Cat2 to the prepolymerized product; wherein the catalyst component Cat1 is selected from the group consisting of the compounds of Ti, Sb and Zn, and mixtures thereof; and the catalyst component Cat2 is selected from the compounds of RE and mixtures thereof.