For tissue engineering applications, the preparation of biodegradable and biocompatible scaffolds is the most desirable but challenging task. Among the various fabrication methods, electrospinning is the most attractive one due to its simplicity and versatility. Additionally, electrospun nanofibers mimic the size of natural extracellular matrix ensuring additional support for cell survival and growth. This study showed the viability of the fabrication of long fibers spanning a larger deposit area for a novel biodegradable and biocompatible polymer named poly(glyceroldodecanoate) (PGD) 1 by using a newly designed collector for electrospinning. PGD exhibits unique elastic properties with similar mechanical properties to nerve tissues, thus it is suitable for neural tissue engineering applications. The synthesis and fabrication set-up for making fibrous scaffolding materials was simple, highly reproducible, and inexpensive. In biocompatibility testing, cells derived from mouse embryonic stem cells could adhere to and grow on the electrospun PGD fibers. In summary, this protocol provided a versatile fabrication method for making PGD electrospun fibers to support the growth of mouse embryonic stem cell derived neural lineage cells.