Disclosed is a process of preparing a biodegradable polymer using an enzyme catalyst and a biodegradable polymer prepared through the process. The process includes polycondensing a polyhydric alcohol monomer having a secondary hydroxyl functional group and an acid monomer having a dicarboxylic group in the presence of the enzyme catalyst. Since the biodegradable polymer according to the present invention is polymerized using an enzyme in the course of the polycondensation, it is easily prepared and friendly to nature, and it is possible to control the molecular weight by varying the reaction time in the course of the polymerization. Thus, the biodegradable polymer is usefully applied to control the dose of a drug in a drug release system and is useful as a supporter for regenerating a desired biological tissue of a patient in tissue engineering.