Touchspinning is a simple and scalable method which does not depend on the dielectric properties of polymer solutions and it has shown advantages over the common fiber spinning techniques, such as electrospinning and microfluidic spinning. Touchspinning setup is used for drawing nano- and microfibers from polymer solutions or melts using a rotating rod or a set of rods. In this study, the aligned touchspun polycaprolactone (PCL) nanofibers were fabricated at different spinning rates and the proliferation potential of the neural stem cells (NSCs) was analyzed on these nanofibrous scaffolds. The aligned electrospun PCL nanofibers were fabricated at spinning rates similar to the touchspun nanofibers and they were served as a control group. The Young's modulus values of the touchspun fibers at various spinning rates were much higher than those of electrospun fibers. Also, the structural characteristics of the PCL nanofibers were analyzed by X-ray diffraction (XRD). The degree of crystallinity of the touchspun fibers was greater than that of electrospun fibers at various spinning rates. The NSC cells exhibited an elongated neurite growth along the touchspun PCL nanofibers with varying spinning rates. Whereas, the NSC cells tend to aggregate on the entangled electrospun PCL nanofibers and they did not spread along the fibers. As the spinning rate of the touchspun nanofibers increased, the percentage of TUJ1 positive cells and the percentage of GFAP positive neurons increased. These results have shown the feasibility of using the touchspinning technique to fabricate fibrous scaffolds for neural tissue engineering applications.