New composite membranes based on porous anodic alumina films and polymer of intrinsic microporosity (PIM-1) have been prepared using a spin-coating technique. According to scanning electron microscopy, partial penetration of polymer into the pores of alumina supports takes place giving rise to selective polymeric layers with fiber-like microstructure. Geometric confinement of rigid PIM-1 in the channels of anodic alumina causes reduction of small-scale mobility in polymeric chains. As a result, transport of permanent gases, such as CH4, becomes significantly hindered across composite membranes. Contrary, the transport of condensable gases (CO2, С4H10), did not significantly suffer from the confinement due to high solubility in the polymer matrix. This strategy enables enhancement of selectivity towards CO2 and C4H10 without significant loss of the membrane performance and seems to be prospective for drain and sweetening of natural gas.