Three-dimensional (3-D) bioprinting is the layer-by-layer deposition of biological material with the aim of achieving stable 3-D constructs for application in tissue engineering. It is a powerful tool for the spatially directed placement of multiple materials and/or cells within the 3-D sample. Encapsulated cells are protected by the bioink during the printing process. Very few materials are available that fulfill requirements for bioprinting as well as provide adequate properties for cell encapsulation during and after the printing process. A hydrogel composite including alginate and gelatin precursors was tuned with different concentrations of hydroxyapatite (HA) and characterized in terms of rheology, swelling behavior and mechanical properties to assess the versatility of the system. Instantaneous as well as long-term structural integrity of the printed hydrogel was achieved with a two-step mechanism combining the thermosensitive properties of gelatin with chemical crosslinking of alginate. Novel syringe tip heaters were developed for improved temperature control of the bioink to avoid clogging. Human mesenchymal stem cells mixed into the hydrogel precursor survived the printing process and showed high cell viability of 85% living cells after 3 days of subsequent in vitro culture. HA enabled the visualization of the printed structures with micro-computed tomography. The inclusion of HA also favors the use of the bioink for bone tissue engineering applications. By adding factors other than HA, the composite could be used as a bioink for applications in drug delivery, microsphere deposition or soft tissue engineering.