Three-dimensional bioprinting holds promise in the anatomical fabrication of lost tissues and organs. Cell-laden hydrogels have been widely used as bioinks, extruded through a nozzle of 3D bioprinter to form the desired shape layer-by-layer. However, the major challenge in 3D bioprinting is finding functional biomaterials to develop bioinks, besides animal-based biomaterials, such as gelatin and collagen. The amine-hyaluronic acid (HA-NH2) was covalently crosslinked with the aldehyde-alginate (Alg-CHO). Once HA-NH2 and Alg-CHO solutions combine, by varying volume ratios, gelation is initiated through a Schiff’s base reaction. The goal of this study was to investigate how volume ratios of HA-NH2 and Alg-CHO had impacts on the printability and biodegradability of the HA-Alg hydrogel and its potential use in the chondrogenic differentiation of mesenchymal stem cells (hMSCs). The HA-Alg hydrogel made from equal volumes of HA-NH2 and Alg-CHO exhibited shear-thinning behaviours, which are essential features of a printable bioink. Moreover, we demonstrated cartilage tissue formation by encapsulating hMSCs in the HA-Alg hydrogel for 4 weeks. To demonstrate a proof-of-concept in creating an interpenetrating polymer network (IPN), the incorporation of silk fibroin into the HA-Alg hydrogel network was tested. This finding allowed the HA-Alg hydrogel to serve as a platform for development of other bioinks, without adverse effects on mechanical properties and shear-thinning behaviours. The results suggest that the HA-Alg hydrogel can be used as a printable biomaterial for the extrusion-based 3D bioprinter. The HA-Alg hydrogel promoted cartilage tissue development and potentially supported other tissue formation due to its tailorable mechanical and degradable properties.