Graphene-coated plastic substrates, such as polyethylene terephthalate (PET), are regularly used in flexible electronic devices. Here we demonstrate a new application of the graphene-coated nanoporous PET membrane for the selective separation of metal ions in an ion exchange manner. Irradiation with swift heavy ions is used to perforate graphene and PET substrate. This process could create graphene nanopores with carboxyl groups, thus forming conical holes in the PET after chemical etching to support graphene nanopores. Therefore, a monolayer nanoporous graphene membrane with a PET substrate is constructed successfully to investigate its ionic selective separation. We find that the permeation ratio of ions strongly depends on the temperature and H+ concentration in the driving solution. An electric field can increase the permeation ratio of ions through the graphene nanopores, but it inhibits the ion selective separation. Moreover, the structure of the graphene nanopore with carboxyl groups is resolved at the density functional theory level. The results show the asymmetric structure of the nanopore with carboxyl groups, and the analysis indicates that the ionic permeation can be attributed to the ion exchange between metal ions and protons on the two sides of graphene nanopores. These results would be beneficial to the design of membrane separation materials made from graphene with efficient online and offline bulk separation.