This work studies the transport properties of solid-state nanopores. Nanopores with a diameter of 35–40 nm formed in a thin “free-standing” silicon nitride membrane of 300 nm thick. An experimental setup has been developed to  study the transport characteristics of single nanopores. Based on the results of electrical measurements, the pore conductivity was calculated for concentrations of KCl electrolyte in the range of 10-4–1M. An increase of nanopore  conductivity was observed with an increase of the electrolyte concentration above 10-2 M. This dependence can be explained by the electrical double layer overlapping that leads to appearance of a charged region inside the  nanopore.