Slowing down DNA translocation speed in a nanopore is essential to ensuring reliable resolution of individual bases. Thin membrane materials enhance spatial resolution but simultaneously reduce the temporal resolution as the molecules translocate far too quickly. In this study, we examined the effect of exposed graphene layers on the transport dynamics of both single (ssDNA) and double-stranded DNA (dsDNA) through nanopores. Following the designs of experimental systems studied by our collaborators at UIUC (Bashir group), we built nanopore systems featuring either a plain dielectric membrane or a dielectric membrane sandwiched between two layers of graphene and simulated the electrophoretic transport of DNA through the nanopores. In qualitative agreement with experiment, we observed a reduction of DNA translocation velocity in the case of graphene-dielectric-graphene membranes produced by hydrophobic interactions of DNA nucleotides and graphene. The simulations have also shown that the translocation of ssDNA through stacked graphene membranes is stepwise, reproducibly placing individual DNA nucleotides at the prescribed locations in the nanopore. Based on these findings, we propose that the integration of multiple stacked graphene layers could slow down DNA enough to enable the identification of nucleobases.