The inadequacies of the currently used small diameter, non-biodegradable synthetic grafts prompt researchers to focus on the design parameters of vascular grafts. Since the purpose is to mimic the native vessel as far as possible, the design parameters are mainly determined by the layout of cell types and proteins in the layers of the vessels and the nano and micro structure of their environments. In consequence of this, the complex structure of native vessels has become a broad source of inspiration for researchers. Electrospun fibrous scaffolds with their well accepted advantages are promising candidates and researchers are able to work with various materials with differing forms, structures, dimensions, and surface modifications according to their requirements. On the other hand, both synthetic biodegradable polymers and natural proteins are the key materials that enable researchers to take one step closer to achieving the goal of creating an autologous vessel at some time after implantation. When the priority and significance of the need for small diameter vascular grafts is considered, the research field to improve vascular grafts is worthy of note. In this regard, the objective of this review is to discuss comparatively the current studies on the design parameters of electrospun vascular grafts, defined as fiber orientation, fiber diameter, pore size and porosity, wall thickness, and material selection, based on the structure of native blood vessels, the requirements of vascular grafts and electrospinning technology, and the advantages of electrospun vascular grafts, to give an outlook for further studies.