A novel robust quaternized poly(styrene-b-isobutylene-b-styrene) (QSIBS)-based anion exchange membrane (AEM) could be achieved via quaternization and cross-linking reaction of chloromethylated SIBS with amines in the presence of graphene sheets grafted with polydimethylsiloxane arc-bridges (G-g-Arc PDMS). The resulting cross-linked QSIBS/G-g-Arc PDMS composite membranes exhibit significantly high ion conductivity (sigma) and dynamic mechanical properties, marked by low methanol permeability, together with improved chemical stability. The a of composite AEM with 0.25 wt% of graphene loading reached remarkably to 1.81 x 10(-2) S cm(-1) at 60 degrees C, compared to that (1.15 x 10(-2) S cm(-1)) of QSIBS. This membrane also behaves high storage modulus of 236 MPa even at 150 degrees C, while Nafion 115 lost its modulus at 150 degrees C. The homogeneous dispersion of G-g-Arc PDMS in QSIBS matrix leads to a great decrease in methanol permeability to 3.81 x 10(-7) cm(2) s(-1), which is much lower than that of Nafion 115.