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A 3D hydrogen-bonded metal-organic framework, [Cu(apc)₂]_n (<b>TJU-Dan-5</b>, Hapc = 2-aminopyrimidine-5-carboxylic acid), was synthesized via a solvothermal reaction. The activated <b>TJU-Dan-5</b> with permanent porosity exhibits a moderate uptake of 1.52 wt% of hydrogen gas at 77 K. The appropriate BET surface areas and decoration of the internal polar pore surfaces with groups that form extensive hydrogen bonds offer a more favorable environment for selective C₂H₆ adsorption, with a predicted selectivity for C₂H₆/CH₄ of around 101 in C₂H₆/CH₄ (5:95, <i>v</i>/<i>v</i>) mixtures at 273 K under 100 kPa. The molecular model calculation demonstrates a C–H···π interaction and a van der Waals host–guest interaction of C₂H₆ with the pore walls. This work provides a strategy for the construction of 3D hydrogen-bonded MOFs, which may have great potential in the purification of natural gas.