We synthesized and evaluated biodegradable and elastomeric polyesters (poly(glycerol sebacate) (PGS)) using polycondensation between glycerol and sebacic acid to form a cross-linked network structure without using exogenous catalysts. Synthesized materials possess good mechanical properties, elasticity, and surface erosion biodegradation behavior. The tensile strength of the PGS was as high as 0.28 ± 0.004 MPa, and Young's modulus was 0.122 ± 0.0003 MPa. Elongation was as high as 237.8 ± 0.64%, and repeated elongation behavior was also observed to at least three times the original length without rupture. The water-in-air contact angles of the PGS surfaces were about 60°. We also analyzed the properties of an electrospray coating of biodegradable PGS on a nitinol stent for the purpose of enhancing long-term patency for the therapeutic treatment of varicose veins disease. The surface morphology and thickness of coating layer could be controlled by adjusting the electrospraying conditions and solution parameters.