The present invention provides a process for preparing biodegradable aliphatic polyester grafted with polyether which comprises a step of ring opening polymerization of a hydrophilic monomer of epoxide-substituted ethyleneglycolmethylether oligomer or ethyleneglycol oligomer, and a biocompatible cyclic monomer forming polymer backbone with the said monomer, and a non-toxic biodegradable polymer prepared therefrom. In accordance with the invention, the graft ratio and molecular weight of polyether in the biodegradable aliphatic polyester can be easily controlled, and the hydrophlicity and crystallinity are also regulated thereby. The biodegradable polymer of the invention has features of minimized protein adhesion and superior softness, due to its hydrophilic side-chain. Accordingly, it can be applied as biomedical polymers such as the matrices for drug delivery system, suture thread, or bioabsorbable and water-soluble polymers.