Current research strives to create sustainable and ecofriendly organic electrode materials (OEMs) due to the rising concerns about traditional inorganic electrode materials that call for substantial resource consumption in battery manufacturing. However, OEMs often exhibit unbalanced performance, with high capacity conflicting with a long lifespan. Herein, a 2D fully conjugated covalent organic framework featuring abundant C═O and C═N groups (HTPT-COF) was strategically synthesized by coupling 2,3,7,8-tetraamino-1,4,6,9-tetraketone with hexaketocyclohexane octahydrate. It stabilizes the enriched active centers by an extended π-conjugated skeleton, thereby affording a high theoretical capacity in conjunction with potential structure stability. To further unlock the barriers of fast charge, the HTPT-COF was interwoven around highly conductive carbon nanotubes, creating a robust core-sheath heterostructure (HTPT-COF@CNT). Consequently, the crafted HTPT-COF@CNT achieves large reversible capacities of 507.7 mA h g-1, high-rate performance (247.8 mA h g-1 at 20.0 A g-1), and long-term durability (1000 cycles). Aiming to streamline the process and cut the cost of battery manufacturing, all-organic symmetric batteries were well fabricated using HTPT-COF@CNT as both cathode and anode, demonstrating high energy/power density (up to 191.7 W h kg-1 and 3800.3 W kg-1, respectively) and long-term stability over 1000 cycles. Such HTPT-COF@CNT represents a promising sustainable electrode that effectively addresses irreconcilable contradictions encountered by OEMs, boosting the development of advanced organic batteries with high capacity and cycling stability.