Three-dimensional bioprinting of biomaterials shows great potential for producing cell-encapsulated scaffolds to repair nerves after injury or disease. For this, preparation of biomaterials and bioprinting itself are critical to create scaffolds with both biological and mechanical properties appropriate for nerve regeneration, yet remain unachievable. This paper presents our study on bioprinting Schwann cell-encapsulated scaffolds using composite hydrogels of alginate, fibrin, hyaluronic acid, and/or RGD peptide, for nerve tissue engineering applications. For the preparation of composite hydrogels, suitable hydrogel combinations were identified and prepared by adjusting the concentration of fibrin based on the morphological spreading of Schwann cells. In bioprinting, the effects of various printing process parameters (including the air pressure for dispensing, dispensing head movement speed, and crosslinking conditions) on printed structures were investigated and, by regulating these parameters, mechanically-stable scaffolds with fully interconnected pores were printed. The performance of Schwann cells within the printed scaffolds were examined in terms of viability, proliferation, orientation, and ability to produce laminin. Our results show that the printed scaffolds can promote the alignment of Schwann cells inside scaffolds and thus provide haptotactic cues to direct the extension of dorsal root ganglion neurites along the printed strands, demonstrating their great potential for applications in the field of nerve tissue engineering.