Three-dimensional bioprinting using a carboxyvinyl polymer (CVP) solution as a support material, alternately extruded with bioink, holds great promise for tissue engineering and regenerative medicine. This approach enables the fabrication of constructs that are sufficiently soft to preserve the functionality of enclosed cells. To evaluate the applicability of this support material and printing method for mesenchymal stem cells (MSCs), we examined the behavior of immortalized human bone marrow-derived MSCs (UE7T-13). This was carried out in constructs printed with bioinks containing 0.5 w/v% phenol-containing hyaluronic acid, 0.1 w/v% phenol-containing gelatin, and 10 U/mL horseradish peroxidase, which were crosslinked by hydrogen peroxide (H₂O₂) supplied from a support material composed primarily of CVP. During the 14 days of culture after printing, UE7T-13 cells enclosed in the printed constructs elongated and proliferated while maintaining high viability (>90%) and metabolic activity. Furthermore, antibody immunostaining revealed that the cells within the constructs maintained the characteristic MSC phenotype (CD44-positive and CD45-negative). Additionally, following osteogenic, adipogenic, and chondrogenic induction, the cells successfully produced lineage-associated products within the constructs, and the amounts of these products were controlled by varying the H₂O₂ concentration (1–10 mM) in the support material. Overall, the use of CVP together with H₂O₂ in the support material, combined with 3D bioprinting, effectively minimized adverse effects on MSC stemness and differentiation potential, while providing a practical strategy for regulating lineage-specific differentiation. These results demonstrate that this method enhances the utility of horseradish peroxidase-containing bioinks and offers great potential for tissue engineering applications.