Bioprinting is a recent technology in tissue engineering used for the design of porous constructs through layer-by-layer deposition of cell-laden material. This technology would benefit from new biomaterials that can fulfill specific requirements for the fabrication of well-defined 3D constructs, such as the preservation of cell viability and adequate mechanical properties. We evaluated the suitability of a novel semi-interpenetrating network (semi-IPN), based on hyaluronic acid and hydroxyethyl-methacrylate-derivatized dextran (dex-HEMA), to form 3D hydrogel bioprinted constructs. The rheological properties of the solutions allowed proper handling during bioprinting, whereas photopolymerization led to stable constructs of which their mechanical properties matched the wide range of mechanical strengths of natural tissues. Importantly, excellent viability was observed for encapsulated chondrocytes. The results demonstrate the suitability of hyaluronic acid/dex-HEMA semi-IPNs to manufacture bioprinted constructs for tissue engineering.