We demonstrate the fabrication of highly transparent conductive networks on a cellulose nanofiber paper, called cellulose nanopaper. Uniform coating of the conductive nanomaterials, such as silver nanowires (AgNWs) and carbon nanotubes, is achieved by simple filtration of their aqueous dispersions through the cellulose nanopaper, which acts as both filter and transparent flexible substrate. The as-prepared AgNW networks on the nanopaper offer sheet resistance of 12 Omega sq.(-1) with optical transparency of 88%, which is up to 75 times lower than the sheet resistance on a polyethylene terephthalate film prepared by conventional coating processes. These results indicate that the 'filtration coating' provides uniformly connected conductive networks because of drainage in the perpendicular direction through paper-specific nanopores, whereas conventional coating processes inevitably cause self-aggregation and uneven distribution of the conductive nanomaterials because of the hard-to-control drying process, as indicated by the well-known coffee-ring effect. Furthermore, the conductive networks are embedded in the surface layer of the nanopaper, showing strong adhesion to the nanopaper substrate and providing foldability with negligible changes in electrical conductivity. This filtration process is thus expected to offer an effective coating approach for various conductive materials, and the resulting transparent conductive nanopaper is a promising material for future paper electronics.