Covalent organic frameworks with designable periodic skeletons and ordered nanopores have attracted increasing attention as promising cathode materials for rechargeable batteries. However, the reported cathodes are plagued by limited capacity and unsatisfying rate performance. Here we report a honeycomb-like nitrogen-rich covalent organic framework with multiple carbonyls. The sodium storage ability of pyrazines and carbonyls and the up-to twelve sodium-ion redox chemistry mechanism for each repetitive unit have been demonstrated by in/ex-situ Fourier transform infrared spectra and density functional theory calculations. The insoluble electrode exhibits a remarkably high specific capacity of 452.0 mAh g, excellent cycling stability (~96% capacity retention after 1000 cycles) and high rate performance (134.3 mAh g at 10.0 A g). Furthermore, a pouch-type battery is assembled, displaying the gravimetric and volumetric energy density of 101.1 Wh kg and 78.5 Wh L, respectively, indicating potentially practical applications of conjugated polymers in rechargeable batteries.