Abstract The grafting of vinylpyridine (VP) or 1‐vinylimidazole (VIm) onto styrene‐diene‐styrene triblock copolymer (polystyrene‐block‐polybutadiene‐block‐polystyrene (SBS) and polystyrene‐block‐polyisoprene‐block‐polystyrene (SIS)) by radiation‐induced graft copolymerization was studied. The cohesive properties of modified styrene‐diene‐styrene copolymers were calculated according to the group contribution method of Fedors. The changes of properties of modified styrene‐diene‐styrene copolymers reduced the gas permeability of oxygen and nitrogen through copolymer membranes, but increased the O2/N2 selectivity. The morphology of polymeric complexed membranes, which were prepared by complexing (N,N′‐disalicylidene ethylenediamine) cobalt(II) (CoS) with modified SIS and SBS, were studied by means of transmission electron microscopy and optical polarizing microscopy. It was found that the gas permeability was related to the morphological structure of modified styrene‐diene‐styrene block copolymer.