Highly conductive, flexible, stretchable and lightweight electrode substrates are essential to meet the future demand on supercapacitors for wearable electronics. However, it is difficult to achieve the above characteristics simultaneously. In this study, ultrafine stainless-steel fibers (with a diameter of ≈30 μm) are knitted into stainless-steel meshes (SSMs) with a diamond structure for the fabrication of textile stretchable electrodes and current collectors. The electrodes are fabricated by utilizing an electrodeposited three-dimensional network graphene framework and poly(3,4-ethylenedioxythiophene) (PEDOT) coating on the SSM substrates via a two-step electrodeposition process, which show a specific capacitance of 77.09 F g−1 (0.14 A g−1) and superb cycling stability (91% capacitance retention after 5000 cycles). Furthermore, the assembled flexible stretchable supercapacitor based on the PEDOT/reduced graphene oxide (RGO)@SSM electrodes exhibits an areal capacitance (53 mF cm−2 at 0.1 mA cm−2), a good cycling stability (≈73% capacitance retention after 5000 cycles), rate capability (36 mF cm−2 at 5 mA cm−2), stretchable stability (≈78% capacitance retention at 10% strain for 500 stretching cycles) and outstanding flexibility and stability under various bending deformations. The assembled supercapacitors can illuminate a thermometer and a light-emitting diode, demonstrating their potential application as stretchable supercapacitors. This simple and low-cost method developed for fabricating lightweight, stretchable and stable high-performance supercapacitors offers new opportunities for future stretchable electronic devices.