Three-dimensional (3D) bioprinting is a rapidly emerging technique in the field of tissue engineering to fabricate extremely intricate and complex biomimetic scaffolds in the range of micrometers. Such customized 3D printed constructs can be used for the regeneration of complex tissues such as cartilage, vessels, and nerves. However, the 3D printing techniques often offer limited control over the resolution and compromised mechanical properties due to short selection of printable inks. To address these limitations, we combined stereolithography and electrospinning techniques to fabricate a novel 3D biomimetic neural scaffold with a tunable porous structure and embedded aligned fibers. By employing two different types of biofabrication methods, we successfully utilized both synthetic and natural materials with varying chemical composition as bioink to enhance biocompatibilities and mechanical properties of the scaffold. The resulting microfibers composed of polycaprolactone (PCL) polymer and PCL mixed with gelatin were embedded in 3D printed hydrogel scaffold. Our results showed that 3D printed scaffolds with electrospun fibers significantly improve neural stem cell adhesion when compared to those without the fibers. Furthermore, 3D scaffolds embedded with aligned fibers showed an enhancement in cell proliferation relative to bare control scaffolds. More importantly, confocal microscopy images illustrated that the scaffold with PCL/gelatin fibers greatly increased the average neurite length and directed neurite extension of primary cortical neurons along the fiber. The results of this study demonstrate the potential to create unique 3D neural tissue constructs by combining 3D bioprinting and electrospinning techniques.