Developing highly active and durable air cathode catalyst is crucial but challenging for rechargeable zinc-air batteries (ZABs). Herein, a large-area, flexible, self-standing carbon membrane encapsulating adjacent Cu/Na dual-atom-sites catalyst is prepared by a scalable solution blow spinning combined pyrolysis strategy. The Cu-N-C site is inspired by the neighboring Na-containing functional group, which enhances O2 adsorption and optimizes the rate-determining step of O2 activation (*O2→*OOH) during the oxygen reduction reaction (ORR) process. Meanwhile, the Cu-N4 sites are encapsulated inside the carbon nanofibers and anchored by the carbon matrix to form a C2-Cu-N4 configuration, reinforcing the stability of the Cu centers. Moreover, the C matrix, anchored with a Na-containing functional group endows its outer shell C with negative charge, rendering the carbon skeletons less susceptible to corrosion by oxygen species and further preventing the dissolution of Cu centers. Under this multi-type regulations, ZAB with CuNa-CF catalyst as the air cathode demonstrates an unprecedentedly long charging/discharging stability for more than 5000 h with no noticeable decay. This remarkable stability improvement represents a critical step in developing Na-inspired Cu-N-C sites to overcome the durability barriers of ZABs for their future practical applications.