Cable bacteria are an emerging class of electroactive organisms that sustain unprecedented long-range electron transport across centimeter-scale distances. The local pathways of the electrical currents in these filamentous microorganisms remain unresolved. Here, the electrical circuitry in a single cable bacterium is visualized with nanoscopic resolution using conductive atomic force microscopy. Combined with perturbation experiments, it is demonstrated that electrical currents are conveyed through a parallel network of conductive fibers embedded in the cell envelope, which are electrically interconnected between adjacent cells. This structural organization provides a fail-safe electrical network for long-distance electron transport in these filamentous microorganisms. The observed electrical circuit architecture is unique in biology and can inspire future technological applications in bioelectronics.