We have carried out Brownian Dynamics calculations to investigate the mechanism of current blockade by double-stranded DNA (dsDNA) in a nanopore. We find that the blockade current crosses over from negative to positive as the ionic concentration decreases, similar to experiment. In addition to the volume exclusion and the counterion condensation, we find that the electric double layer overlap is a significant factor in the Current blockade. The electric double layer overlap causes the ionic concentration beyond the immediate neighborhood of dsDNA and the wall to be lower in a dsDNA-blocked nanopore than the plateau ionic concentration away from the wall in an open nanopore, thus contributing importantly to the blockade current. On the basis of the calculated ion distribution function in the nanopore, we examined the counterion condensation to the dsDNA. We find the excess counterion condensation to be about 60% of the charge on the dsDNA, which is within the range of percentages obtained from experiments. We performed equilibrium and nonequilibrium (under an applied electric field) Brownian dynamics Simulations to calculate the average mobility of the ions in nanopores. The calculated ion mobility is found to be reduced in DNA-blocked nanopores.