We report an extrusion-based bioprinting approach, in which stabilization of extruded bioink is achieved through horseradish peroxidase (HRP)-catalyzed cross-linking consuming hydrogen peroxide (H2O2) supplied from HRP and glucose. The bioinks containing living cells, HRP, glucose, alginate possessing phenolic hydroxyl (Ph) groups, and cellulose nanofiber were extruded to fabricate 3D hydrogel constructs. Lattice- and human nose-shaped 3D constructs were successfully printed and showed good stability in cell culture medium for over a week. Mouse 10T1/2 fibroblasts enclosed in the printed constructs remained viable after 7 days of culture. It was also able to switch a non-cell-adhesive surface of the printed construct to cell-adhesive surface for culturing cells on it through a subsequent cross-linking of gelatin possessing Ph moieties. These results demonstrate the possibility of utilizing the presented cross-linking method for 3D bioprinting.