One recent application of nanopores is to use them as detectors and analyzers for fast DNA sequencing. To better understand the DNA electrokinetic transport through a nanopore, a hydrodynamic model is developed to investigate the flow field, the resistive forces acting on the DNA, the DNA velocity and the ionic current through the nanopore. The numerical results reveal the relation between the DNA velocity and various parameters such as nanopore surface charge and solution concentration. The model is validated by comparing the numerical results with the experimental data for both DNA velocity and ionic current through the nanopore.