Electro‐conductive nanofiber networks have potential applications as gas diffusion electrodes (GDEs) operating at solid–liquid-gas three‐phase interfaces. Flexible GDEs are developed, based on a versatile method of conformally coating a Cu layer on membranes consisting of stacked electrospun nonconductive polymer nanofibers. The Cu coating, comprising fine‐grained Cu crystals, has an average thickness of circa 50 nm and a root‐mean‐square roughness of circa 5.3 nm, maintaining the topography of polymer nanofibers. For nanofiber membranes with a thickness ranging in a few micrometers, the conformal Cu layer coats all nanofibers in the outermost layers as well as in the bulk of the membrane. All demonstrated Cu‐coated nanofiber networks have sheet resistance <2.4 Ω_◽, and gas permeability in the order of 10^-13 to 10^-15 m², which are comparable to some commercialized carbon based micro‐/nanofiber GDEs. Particularly, these conductive nanofiber networks have excellent bending durability, with negligible conductivity degradation after 10 000 bending test cycles. The high conductivity, gas permeability, and flexibility of these 3D nanofiber networks allow for applications as GDEs into various flexible electrochemical devices.