Experimental evidence revealed that the performance of nanopore-based biosensing devices can be improved by applying a salt concentration gradient. To provide a theoretical explanation for this observation and explore the mechanisms involved, we model the capillary osmosis (or diffusioosmosis) in a charged solid-state nanopore connecting two large reservoirs. The effects of nanopore geometry and the reservoir salt concentrations are examined. We show that the capillary osmotic flow is from the high salt concentration reservoir to the low salt concentration one, and its magnitude has a maximum as the reservoir salt concentrations vary. In general, the shorter the nanopore and/or the smaller its radius, the faster the osmotic flow. This flow enhances the current recognition, and the ion concentration polarization across nanopore openings raises the entity capture rate, thereby being capable of improving the performance of electrophoresis-based biosensors. The results gathered provide necessary information for designing nanopore-based biosensor devices.