Hydrogels are particularly attractive as scaffolding materials for cartilage tissue engineering because their high water content closely mimics the native extracellular matrix (ECM). Hydrogels can also provide a three-dimensional (3D) microenvironment for homogeneously suspended cells that retains their rounded morphology and thus facilitates chondrogenesis in cartilage tissue engineering. However, fabricating hydrogel scaffolds or cell-laden hydrogel constructs with a predesigned external shape and internal structure that does not collapse remains challenging because of the low viscosity and high water content of hydrogel precursors. Here, we present a study on the fabrication of (cell-laden) alginate hydrogel constructs using a 3D bioplotting system supplemented with a submerged cross-linking process. Swelling, mechanical properties and protein release profiles were examined and tuned by controlling the initial cross-linking density. Porous cell-laden alginate hydrogel constructs were also fabricated and cell viability, cell proliferation, and cartilaginous ECM deposition were investigated. The fabrication technique and the hydrogel scaffolds obtained supported high cell viability and the deposition of cartilaginous ECM, demonstrating their potential for applications in the field of cartilage tissue engineering.