We here present a laser-patterning method that may solve the visibility problem associated with silver nanowire (AgNW) transparent electrodes. In conventional methods, AgNW electrodes are patterned on a transparent substrate by either selective removal or deposition of the material. Therefore, the fabricated pattern becomes visible due to the difference in transmittance/reflectance between the regions with and without AgNWs. Our approach is to disconnect the AgNW networks in selective areas by a laser and thus make the irradiated areas electrically insulating. This method is fundamentally based on Rayleigh instability. Given that the laser-cut nanowires remain on the substrate, the electrode pattern fabricated by the method can be invisible. The feasibility of the presented approach is demonstrated by fabricating organic light-emitting diodes using patterned AgNW electrodes and then characterizing their performance capabilities.