Vascular regeneration is a complex process, additionally limited by the low regeneration potential of blood vessels. Hence, current research is focused on the design of artificial materials that combine biocompatibility with a certain rate of biodegradability and mechanical robustness. In this paper, we have introduced a scaffold material made of poly(L-lactide-co-glycolide)/poly(isosorbide sebacate) (PLGA/PISEB) fibers fabricated in the course of an electrospinning process, and confirmed its biocompatibility towards human umbilical vein endothelial cells (HUVEC). The resulting material was characterized by a bimodal distribution of fiber diameters, with the median of 1.25 µm and 4.75 µm. Genotyping of HUVEC cells collected after 48 h of incubations on the surface of PLGA/PISEB scaffolds showed a potentially pro-angiogenic expression profile, as well as anti-inflammatory effects of this material. Over the course of a 12-week-long hydrolytic degradation process, PLGA/PISEB fibers were found to swell and disintegrate, resulting in the formation of highly developed structures resembling seaweeds. It is expected that the change in the scaffold structure should have a positive effect on blood vessel regeneration, by allowing cells to penetrate the scaffold and grow within a 3D structure of PLGA/PISEB, as well as stabilizing newly-formed endothelium during hydrolytic expansion.