Neural tissue engineering is one of the most promising approaches for healing nerve damage, which bypasses the limits of contemporary conventional treatments. In a previous study, we developed a fibrous scaffold via electrospinning poly (glycerol dodecanedioate) (PGD) and gelatin that mimics the structure of a native extracellular matrix (ECM) for soft tissue engineering application. In this study, fumaric acid (FA) was incorporated into the PGD synthesis process, which produced a PGD derivative referred to as poly (glycerol dodecanedioate co-fumarate) (PGDF). This introduced a new functional group, a double bond, into the polymer thus providing new modification possibilities. Arg-Gly-Asp-Cys (RGDC) and laminin peptides were chosen as biomolecules to modify the fiber and facilitate cell attachment and differentiation efficiency. The release of FA into the medium was quantified to investigate the bioreactivity of the derived scaffolds. In combination with UV crosslinking, the developed PGDF fiber mats were able to withstand degradation processes for up to 2 months, which ensures that neural tissue engineering applications are viable. Cell viability and motor neuron differentiation efficiency were demonstrated to be significantly improved with the addition of FA, RGDC and laminin peptides.