A series of nanopores with diameters ranging from 2.5 to 63 nm are fabricated on a reduced Si3N4 membrane by focused ion beam and high energy electron beam. Through measuring the blocked ionic currents for DNA strands threading linearly through those solid-state nanopores, it is found that the blockade ionic current is proportional to the square of the hydrodynamic diameter of the DNA strand. With the nanopore diameter reduced to be comparable with that of DNA strands, the hydrodynamic diameter of the DNA becomes smaller, which is attributed to the size confinement effects. The duration time for the linear DNA translocation events increases monotonically with the nanopore length. By comparing the spatial configurations of DNA strands through nanopores with different diameters, it is found that the nanopore with large diameter has enough space to allow the DNA strand to translocate through with complex conformation. With the decrease of the nanopore diameter, the folded part of the DNA is prone to be straightened by the nanopore, which leads to the increase in the occurrence frequency of the linear DNA translocation events. Reducing the diameter of the nanopore to 2.5 nm allows the detection and discrimination of three nucleotide "G" and three nucleotide "T" homopolymer DNA strands based on differences in their physical dimensions.