Biodegradable polyester elastomers are widely reported to be applied in varied biomedical fields. In this paper, we attempt to investigate how both the thermal-curing time and molar ratio of the monomers affect the final compositions and properties of the novel poly(glycerol-sebacate-citrate) (PGSC) elastomers. First, PGSC elastomers are obtained after the thermal curing of the moldable mixtures consisting of citric acid and poly(glycerol-sebacate) (PGS) prepolymers synthesized in the lab. Then further studies show that, on the one hand, the control of longer thermal-curing time results in elastomers with less sol, lower swelling degree, slower degradation, greater mechanical strength and higher glass transition temperature and, on the other hand, the crosslink with more citric acid is advantageous to greatly improving their mechanical strength and glass transition temperatures, simultaneously decreasing their sol contents, swelling degrees and degradation rates. The PGSC elastomers show thermosetting properties, certain strength, mass losses lower than 20% after 4-week degradation and durative water absorption during degradation. Thus they might be potentially used as degradable bio-coatings, varied soft biomedical membranes and drug delivery matrices.