Novel transparent conductive electrodes (TCEs) with copper (Cu)/silver (Ag) core/shell nanofibers (NFs) containing random, aligned, and crossed structures were prepared using a combination of electrospinning (ES) and chemical reduction. The ES process was used to prepare continuous copper nanofibers (Cu-NFs), which were used as core materials and were then immersed in silver ink (Ag ink) to form a protective layer of Ag to protect the Cu-NFs from oxidation. The Ag shell layer protected the Cu-NFs against oxidation and enhanced their conductivity. Such Cu/Ag core/shell webs can be easily transferred on the flexible matrix and can be applied in TCEs. The metal NF webs of different structures exhibited various degrees of conductivity and followed the order random type > crossed type > aligned type; however, the order with respect to transmittance (T) was inverse. The aligned nanowire networks exhibited a high T of over 80%, and the random ones exhibited a low sheet resistance of less than 102 Ω/sq (the best value is 7.85 Ω/sq). The present study demonstrated that TCEs based on Cu/Ag core/shell NF webs have considerable flexibility, transparency, and conductivity and can be applied in novel flexible light-emitting diode devices and solar cells in the future.