The introduction of 3D bioprinting is expected to revolutionize the field of tissue engineering and regenerative medicine. The 3D bioprinter is able to dispense materials while moving in X, Y, and Z directions, which enables the engineering of complex structures from the bottom up. In this study, a bioink that combines the outstanding shear thinning properties of nanofibrillated cellulose (NFC) with the fast cross-linking ability of alginate was formulated for the 3D bioprinting of living soft tissue with cells. Printability was evaluated with concern to printer parameters and shape fidelity. The shear thinning behavior of the tested bioinks enabled printing of both 2D gridlike structures as well as 3D constructs. Furthermore, anatomically shaped cartilage structures, such as a human ear and sheep meniscus, were 3D printed using MRI and CT images as blueprints. Human chondrocytes bioprinted in the noncytotoxic, nanocellulose-based bioink exhibited a cell viability of 73% and 86% after 1 and 7 days of 3D culture, respectively. On the basis of these results, we can conclude that the nanocellulose-based bioink is a suitable hydrogel for 3D bioprinting with living cells. This study demonstrates the potential use of nanocellulose for 3D bioprinting of living tissues and organs.