A molecular dynamics simulation method is used to study the translocation of a single strand DNA through nanopores opened on graphene membranes. Simulation results uncover that the translocation time for four DNA strands (20G, 20A, 20T, and 20C) is proportional to the size of the four DNA bases. However, the change of the ionic current is caused not only by the physical blockade of the DNA, but also induced by the change of the ion distribution once the negatively charged DNA enters the nanopore. An electric double layer will be formed and causes higher cation and lower anion concentration near the DNA strand surface, which makes the ionic current blockade not sensitive to the base size for a single-layer graphene nanopore. Increasing the graphene membrane thickness can enhance the DNA physical blockage effect on ionic current and improve the nanopore sensitivity to the four DNA bases.