Amine-containing mixed-matrix membranes incorporated with amino-functionalized multi-walled carbon nanotubes (AF-MWNTs) were synthesized for CO₂/H₂ separation based on the facilitated transport mechanism. AF-MWNTs were chosen primarily as the mechanical reinforcing filler to enhance the membrane stability. At 107 °C and 0.2-MPa feed pressure, the membrane incorporated with 10 wt.% AF-MWNTs showed a CO₂ permeability of 3196 Barrers and a CO₂/H₂ selectivity of 205. At the higher feed pressure of 1.5 MPa, owing to the carrier saturation phenomenon, the same membrane exhibited reduced transport performance with a CO₂ permeability of 776 Barrers and a CO₂/H₂ selectivity of 31. These separation performances at both the low and high feed pressures were well above the theoretical upper bound. Furthermore, the incorporation of 10 wt.% AF-MWNTs led to a significant improvement on membrane stability. The transport performance and selective layer thickness of this membrane maintained for 100 h, which suggested that the incorporation of AF-MWNTs improved the resistance to membrane compaction upon a high feed pressure. Therefore, this work is considered as one of the crucial steps to enable the application of facilitated transport membranes to high-pressure gas processing such as syngas purification.