Tooth decay is one of the most common chronic disorders throughout the world. Regenerating decayed dentin/pulp structure requires the design of novel scaffolding materials that mimic the architecture of a natural dental extracellular matrix (ECM) and provide suitable environments for the attachment, proliferation, differentiation, and biomineralization of dental pulp stem cells (DPSCs). In this work, we developed an approach to prepare three-dimensional (3D) nano-fibrous gelatin/silica bioactive glass (NF-gelatin/SBG) hybrid scaffolds that mimic the nano-structured architecture and chemical composition of a natural dental ECM. This approach involved the combination of a thermally induced phase separation, sol–gel, and porogen leaching process, and synthesized hybrid scaffolds possessing natural ECM-like architecture, high porosity, well-defined pore size and interconnectivity, and improved mechanical strength. An in vitro cell culture study showed that human DPSCs had a significantly higher proliferation rate on NF-gelatin/SBG scaffolds compared to NF-gelatin scaffolds under the same conditions. Furthermore, the integration of SBG into the hybrid scaffold significantly promoted the differentiation and biomineralization of the human DPSCs. The alkaline phosphatase (ALP) activity and expressions of marker genes for odontogenic differentiation (Col I, ALP, OCN, DSPP and DMP-1) were all significantly higher in the NF-gelatin/SBG than in the NF-gelatin group. Those results were further confirmed by hematoxylin and eosin (H&E) and von Kossa staining, as evidenced by greater ECM secretion and mineral deposition in the hybrid scaffold. In summary, the biomimetic NF-gelatin/SBG hybrid scaffolds provide an excellent environment for the growth and differentiation of human DPSCs and are promising candidates for dentin/pulp tissue regeneration.