A novel polyethyleneimine (PEI)-loaded Fe-doped Cu₂(OH)PO₄ adsorbent was synthesized via physical impregnation and characterized using XRD, FT-IR, SEM, XPS, and N₂ adsorption. Key parameters (Fe doping, PEI loading, temperature, flow rate) affecting CO₂ adsorption were optimized using the response surface methodology (RSM, Box–Behnken design), and flow rate was identified as the most influential factor. The optimal adsorbent, 8 %Fe–Cu₂(OH)PO₄@50 %PEI, achieved a CO₂ adsorption capacity of 3.95 mmol/g (60 °C, 30 ml/min). A significant synergistic effect (α = 3.2426) existed between Fe doping and PEI loading. RSM predictions (8.8 mol %Fe, 50.6 wt % PEI, 50.1 °C, 28 ml/min; capacity 3.95 mmol/g) closely matched those obtained in the experiment (3.90 mmol/g). The adsorbent exhibited excellent stability over 20 cycles (capacity loss: 0.35 mmol/g). Kinetic and thermodynamic studies indicated barrier-free (E_a = −41.66 kJ/mol), exothermic, spontaneous, and entropy-driven monolayer adsorption. This demonstrates that 8 %Fe–Cu₂(OH)PO₄@50 %PEI is a highly efficient and recyclable CO₂ adsorbent.