For tissue engineering applications, biodegradable scaffolds play a vital role in supporting and guiding the seeded cells to form functional tissues by mimicking the structure and function of native extracellular matrices. Previously, we have developed a biodegradable elastomer poly (glycerol-dodecanedioate) (PGD) with mechanical properties suitable for soft tissue engineering. In the study, we found that the PGD and PGD blended with gelatin (PGD/gelatin) were able to be electrospun into fibrous scaffolds, and the diameters of the fibers could be adjusted by controlling the PGD concentration. When using our newly designed electrospinning collector, fibers could be easily harvested and the size of the fiber mat could be flexibly adjusted. The data of Raman spectra also confirmed the esterfication reaction in PGD polymerization and showed no significant structure change after electrospinning. Biocompatibility testing of the PGD and PGD/gelatin, by using human foreskin fibroblasts, indicated that gelatin could enhance cell adhesion and proliferation. Overall, electrospun fibers made from PGD and PGD/gelatin exhibited several advantages including easy synthesis from renewable raw materials, flexible fabrication by using less toxic solvents like ethanol, and good biocompatibility.