On the basis of the reaction between ketene and alcohol groups to result in an ester linkage and Meldrum's acid as an effective precursor of ketene group, a bifunctional aliphatic Meldrum's acid compound (BisMA) is synthesized and used as a monomer to react with ethylene glycol and glycerol for the preparation of linear and cross-linked aliphatic polyesters, respectively. A 62 and 35 wt % of biodegradation fraction have been recorded on the linear and cross-linked aliphatic polyesters after an 8 week biodegradation test, respectively, to demonstrate the good biodegradability of the synthesized polyesters. In addition to conventional linear biodegradable polyesters, this synthetic route also provides a new and convenient method for preparation of cross-linked biodegradable polyesters. The types of the required monomers and reaction methods for preparation of the cross-linked biodegradable polyesters are similar to those used for conventional thermosetting resins. An integration of biodegradable polymers and thermosetting resins in polymer chemistry has been demonstrated.