Emerging rechargeable aluminium batteries (RABs) offer a sustainable option for next-generation energy storage technologies with low cost and exemplary safety. However, the development of RABs is restricted by the limited availability of high-performance cathode materials. Herein, we report two polyimide two-dimensional covalent organic frameworks (2D-COFs) cathodes with redox-bipolar capability in RAB. The optimal 2D-COF electrode achieves a high specific capacity of 132 mAh g⁻¹. Notably, the electrode presents long-term cycling stability (with a negligible ≈0.0007 % capacity decay per cycle), outperforming early reported organic RAB cathodes. 2D-COFs integrate n-type imide and p-type triazine active centres into the periodic porous polymer skeleton. With multiple characterizations, we elucidate the unique Faradaic reaction of the 2D-COF electrode, which involves AlCl²⁺ and AlCl₄⁻ dual-ions as charge carriers. This work paves the avenue toward novel organic cathodes in RABs.