Membrane-based　gas　separation　exhibits　many　advantages　over　other　conventional　techniques;　however,　the　construction　of　membranes　with　simultaneous　high　selectivity　and　permeability　remains　a　major　challenge.　Herein,　(LDH/FAS)(n)-PDMS　hybrid　membranes,　containing　two-dimensional　sub-nanometre　channels　were　fabricated　via　self-assembly　of　unilamellar　layered　double　hydroxide　(LDH)　nanosheets　and　formamidine　sulfinic　acid　(FAS),　followed　by　spray-coating　with　a　poly(dimethylsiloxane)　(PDMS)　layer.　A　CO2　transmission　rate　for　(LDH/FAS)(25)-PDMS　of　7748　GPU　together　with　CO2　selectivity　factors　(SF)　for　SF(CO2/H-2),　SF(CO2/N-2)　and　SF(CO2/CH4)　mixtures　as　high　as　43,　86　and　62　respectively　are　observed.　The　CO2　permselectivity　outperforms　most　reported　systems　and　is　higher　than　the　Robeson　or　Freeman　upper　bound　limits.　These　(LDH/FAS)(n)-PDMS　membranes　are　both　thermally　and　mechanically　robust　maintaining　their　highly　selective　CO2　separation　performance　during　long-term　operational　testing.　We　believe　this　highly-efficient　CO2　separation　performance　is　based　on　the　synergy　of　enhanced　solubility,　diffusivity　and　chemical　affinity　for　CO2　in　the　sub-nanometre　channels.　Membrane-based　gas　separation　exhibits　many　advantages　over　other　conventional　techniques　but　the　construction　of　membranes　with　simultaneous　high　selectivity　and　permeability　remains　a　major　challenge.　Here,　the　authors　propose　a　layered　double　hydroxide　(LDH)-polymer　hybrid　membrane,　which　shows　improved　CO2　permselectivity.