The three-dimensional (3D) printed scaffolds were prepared by partial cross-linking of TEMPO-oxidized cellulose nanofibril/alginate hydrogel using calcium ions for printing the hydrogel while maintaining its shape, fidelity, and preventing the collapse of the filaments. The prepared scaffolds were fully cross-linked using calcium ions immediately after printing to provide the rigidity of the hydrogel and give it long-term stability. The composition of the prepared pastes was adjusted in view of the description of the hydrogel and 3D printing parameters. The rheological properties in terms of thixotropic behavior and viscosity recovery of hydrogels were investigated by performing steady shear rate experiments. The results show that the viscosity recovery for pure alginate hydrogel was only about 16% of the initial value, whereas it was 66% when adding cellulose nanofibrils to alginate. Consequently, the shape of the pure alginate scaffold was soft and easy to collapse contrarily to the composite scaffold. The biomimetic mineralization process of printed scaffolds using simulated body fluid, mimicking the inorganic composition of human blood plasma, was performed and the hydroxyapatite nucleation on the hydrogel was confirmed. The strength properties of the fabricated scaffolds in terms of compressive strength analysis were also investigated and discussed. The results show that the alginate/TEMPO-oxidized cellulose nanofibril system may be a promising 3D printing scaffold for bone tissue engineering.