We demonstrate that voltage-biased solid-state nanopores can transiently localize DNA in an electrolyte solution. A double-stranded DNA (dsDNA) molecule is trapped when the electric field near the nanopore attracts and immobilizes a non-end segment of the molecule across the nanopore orifice without inducing a folded molecule translocation. In this demonstration of the phenomenon, the ionic current through the nanopore decreases when the dsDNA molecule is trapped by the nanopore. By contrast, a translocating dsDNA molecule under the same conditions causes an ionic current increase. We also present finite-element modeling results that predict this behavior for the conditions of the experiment.