Redox-active organic materials have gained growing attention as electrodes of rechargeable batteries. However, their key limitations are the low electronic conductivity and limited chemical and structural stability under redox conditions. Herein, we report a new cobalt-based 2D conductive metal-organic framework (MOF), Co-HAB, having stable, accessible, dense active sites for high-power energy storage device through conjugative coordination between a redox-active linker, hexaaminobenzene (HAB), and a Co(II) center. Given the exceptional capability of Co-HAB for stabilizing reactive HAB, a reversible three-electron redox reaction per HAB was successfully demonstrated for the first time, thereby presenting a promising new electrode material for sodium-ion storage. Specifically, through synthetic tunability of Co-HAB, the bulk electrical conductivity of 1.57 S cm-1 was achieved, enabling an extremely high rate capability, delivering 214 mAh g-1 within 7 min or 152 mAh g-1 in 45 s. Meanwhile, an almost linear increase of the areal capacity upon increasing active mass loading up to 9.6 mg cm-2 was obtained, demonstrating 2.6 mAh cm-2 with a trace amount of conducting agent.