Injectable hydrogels have been considered as promising materials for bone regeneration, but their osteoinduction and mechanical performance are yet to be improved. In this study, a novel biocompatible injectable and self-healing nano hybrid hydrogel was on-demand prepared via a fast (within 30 s) and easy gelation approach by reversible Schiff base formed between-CH=O of oxidized sodium alginate (OSA) and-NH2 of glycol chitosan (GCS) mixed with calcium phosphate nanoparticles (CaP NPs). Its raw materials can be ready in large quantities by a simple synthesis process. The mechanical strength, degradation and swelling behavior of the hydrogel can be readily controlled by simply controlling the molar ratio of -CH=O and -NH2. This hydrogel exhibits pH responsiveness, good degradability and biocompatibility. The hydrogel used as the matrix for mesenchymal stem cells can significantly induce the proliferation, differentiation and osteoinduction in vitro. These results showed this novel hydrogel is an ideal candidate for applications in bone tissue regeneration and drug delivery.