The structure design and atomic modulation of catalysts are two sides of the same coin, both of which are deemed critical factors to regulate the intrinsic electrocatalytic activity. Herein, cobalt single‐atom anchored on nitrogen‐doped graphene‐sheet@tube (CoSAs‐NGST) is derived from a novel Co, Zn‐coordinated zeolitic imidazolate framework (CoZn‐ZIF) in the presence of dicyandiamide. CoSAs‐NGST exhibited a hybrid structure with a bamboo‐like graphene tube and sheet. The atomic configuration of intrinsic defects is characterized by electron energy loss spectroscopy. The morphology differentiation from cake‐shape structure to low‐dimension hybrid not only enhances the dispersity of single atoms but also induces defect state evolution, which results in the formation of a CoN4‐rich graphene tube. Density functional theory (DFT) modeling revealed that the coupling effect on oxygen reduction reaction and oxygen evolution reaction (ORR/OER) pathways of Co‐N4‐tube and Co‐N4‐sheet is responsible for the enhanced activity of CoSAs‐NGST. In addition to the superb ORR/OER bifunctional catalytic performance, CoSAs‐NGST also demonstrates a notably small charge–discharge voltage drop of 0.93 V when applied in the rechargeable zinc–air battery outperforming Pt/C + RuO2 catalyst. The present study provides an insight into the relationship between the structure design and atomic modulation of the carbon based catalysts. CoSAs‐NGST is derived from a novel edge‐rich CoZn‐ZIF. The continuous structure differentiation from bulk to low‐dimension hybrid induces electric structure evolution simultaneously. A coupling effect on the reaction pathway of oxygen reduction reaction and oxygen evolution reaction is confirmed. A CoSAs‐NGST based zinc–air battery demonstrates superior performance compared with that of Pt/C + RuO2 catalyst.