Tissue and biomedical engineering fields are in constant mutation and in searching for innovative processing techniques capable to tailor the material properties. In this work, poly(l-lactic acid) (PLLA) and elastomeric poly(glycerol sebacate) (PGS) were dissolved in the same solvents and electrospun together, in a single needle system. A core-shell structure where the hydrophilic PGS was placed onto the surface of the hydrophobic PLLA fibre was obtained for elastomeric concentrations up to 25 wt%. It was found that the PLLA:PGS blends are immiscible and the blends present the melting temperatures of the individual polymers. Moreover, their surface properties were deeply influenced by the presence of the PGS, and a superhydrophilic membrane was obtained, after PGS curing at 120 °C for 48 h. When the concentration of PGS is up to 25 wt%, the blend’s Young modulus decreases from ∼35.9 ± 7.1 to 7.5 ± 1.4 MPa and a twofold improvement in the sample stretchability was observed, compared with the pristine PLLA electrospun samples. Finally, in vitro hypothalamus A59 nerve cell culture shows that the core-shell electrospun samples enhanced cell adhesion and proliferation, suggesting that these developed materials have great potentials for nerve regeneration and biomedical engineering applications.