A graphene-based membrane and a method of producing the same are disclosed. The graphene-based membrane may include a graphene-polymer composite, wherein the graphene-polymer composite may consist of an amine functionalized graphene and a polymer containing an anhydride group as a linker for linking the amine functionalized graphene to the polymer. The graphene-based membrane may be constructed of a single-layer. A method may include reacting a polymer containing an anhydride with an amine functionalized graphene in presence of a solvent to form an intermediate product; and thermal imidizing the intermediate product to form a graphene grafted polymer composite for use in fabricating a graphene-based membrane.