Bioprinting of most cell-laden hydrogel scaffolds with the required structural integrity, mechanical modulus, cell adhesion, cell compatibility, and chondrogenic differentiation are still significant issues that affect the application of bioinks in cartilage tissue engineering. This study focuses on constructing printable bioinks by combining adipose-derived stem cells (ADSCs), hyaluronic acid (HA)-based hydrogels and analyzing their ability to induce chondrogenesis using 3D bioprinting technology. First, biotinylated hyaluronic acid was synthesized via an adipic acid dihydrazide (ADH) linker with amide bond formation to form HA-biotin (HAB). Both HAB and the as-received streptavidin were mixed to form a partially cross-linked HA-biotin-streptavidin (HBS) hydrogel through noncovalent bonding. After that, the partially cross-linked HBS hydrogel was mixed with sodium alginate and subsequently printed to form the HBSA hydrogel 3D scaffolds using a bioprinter. Finally, the 3D scaffolds of the HBSA (HBS + alginate) hydrogel were submerged into CaCl solution to achieve a stable 3D HBSAC (HBSA + Ca) hydrogel scaffold through ion transfer crosslinking. The physical-chemical characteristics of the hybrid bioink compositions have been evaluated to determine the desired 3D bioprinting structure. Cytotoxicity and chondrogenic differentiation were also assessed to confirm that the double cross-linked HBSAC hydrogel scaffold was useful for chondrogenic formation. The results showed that partially crosslinking the biotinylated HA-based hydrogel with streptavidin has a significant effect on printability and structural integrity. Morphological analysis of a suitable 3D printed HBSAC hydrogel scaffold showed visible pores with the desired shape and geometry. We have concluded that the HBSAC hydrogel possesses a favorable biocompatibility profile. The HBSAC hydrogel can also secrete significantly higher amounts of chondrogenic marker genes at day 5 and sulfated glycosaminoglycans (sGAGs) from days 7 to 14 compared to the HA hydrogel, as determined via quantitative real-time PCR assay and Alcian blue staining and the DMMB assay.