Sustainable sodium‐ion batteries (SIBs) have gained tremendous attention; however, the large‐sized Na+ poses serious challenges on the development of inorganic‐based cathodes. To overcome the issues, metal–organic electrode materials are appealing because they combine attractive characteristics of organic redox centers (e.g., flexibility, highly reversible redox properties, fast kinetics (regardless of size and charge of guest ions), structural/redox tunability, and resource abundance) with structural stability arising from metal‐ligand coordination. Herein, a one‐dimensional copper‒benzoquinoid coordination polymer (CP), [CuL(Py)2]n, (LH4 = 1,4‐dicyano‐2,3,5,6‐tetrahydroxybenzene, Py = pyridine) is investigated as cathode for SIBs. As opposed to most CPs reported for SIBs which possess high porosity and surface area, this close‐packed CP can deliver discharge capacity as high as 277 mAh g‒1 at 2C (~523 mA g‒1), and at extremely high rates of 50C and 300C (~13 and 78 A g‒1), reversible capacities of 131 and 74 mAh g‒1 still can be delivered, respectively. The transport kinetics of Na+ in [CuL(Py)2]n is found to be even faster than that of Li+ despite the close‐packed structure. The mechanistic and kinetic studies have been performed. The findings gained in this work undoubtedly unravel a potential design strategy for high‐performance metal–organic electrode materials for emerging post‐Li‐ion batteries.