Efficient and sustainable methods for carbon dioxide capture are highly sought after. Mature technologies involve chemical reactions that absorb CO_2,but they have many drawbacks. Energy-efficient alternatives may be realised by porous physisorbents with void spaces that are complementary in size and electrostatic potential to molecular CO₂. Here, we present a robust, recyclable and inexpensive adsorbent termed MUF-16. This metal-organic framework captures CO₂with a high affinity in its one-dimensional channels, as determined by adsorption isotherms, X-ray crystallography and density-functional theory calculations. Its low affinity for other competing gases delivers high selectivity for the adsorption of CO₂over methane, acetylene, ethylene, ethane, propylene and propane. For equimolar mixtures of CO₂/CH₄and CO₂/C₂H₂, the selectivity is 6690 and 510, respectively. Breakthrough gas separations under dynamic conditions benefit from short time lags in the elution of the weakly-adsorbed component to deliver high-purity hydrocarbon products, including pure methane and acetylene.