Carbon capture and utilization (CCU) technologies, such as CO₂ methanation, generally require energy-intensive CO₂ capture and separation processes prior to catalytic CO₂ conversion. In contrast, integrated CO₂ capture and reduction (CCR) technologies that use dual function materials (DFM) can directly convert low-concentration CO₂ in flue gas or atmosphere into high-concentration CH₄ or CO. In this study, we demonstrate a circulating fluidized bed (CFB) approach to enable continuous operation of CCR. In the CFB approach, the DFM (Na/Ni/Al₂O₃) circulates between two bubbling fluidized beds to enable steady-state cyclic operation of (1) selective capture of CO₂ in flue gas/air and (2) hydrogenation of the captured CO₂. We succeeded in the continuous synthesis of CH₄ with high CO₂ capture efficiency (>88 %) and high H₂ conversion (>85 %) yielding mainly CH₄ (selectivity > 99 %) as the product at high concentration (>20 % CH₄) using 2 % CO₂/N₂ as the model flue gas.