This paper reports the fabrication of scaffolds consisting of radially aligned poly(ε-caprolactone) nanofibers by utilizing a collector composed of a central point electrode and a peripheral ring electrode. This novel class of scaffolds was able to present nanoscale topographic cues to cultured cells, directing and enhancing their migration from the periphery to the center. We also established that such scaffolds could induce faster cellular migration and population than nonwoven mats consisting of random nanofibers. Dural fibroblast cells cultured on these two types of scaffolds were found to express type I collagen, the main extracellular matrix component in dural mater. The type I collagen exhibited a high degree of organization on the scaffolds of radially aligned fibers and a haphazard distribution on the scaffolds of random fibers. Taken together, the scaffolds based on radially aligned, electrospun nanofibers show great potential as artificial dural substitutes and may be particularly useful as biomedical patches or grafts to induce wound closure and/or tissue regeneration.