Conjugated polymeric molecules have been heralded as promising electrode materials for the next-generation energy-storage technologies owing to their chemical flexibility at the molecular level, environmental benefit, and cost advantage. However, before any practical implementation takes place, the low capacity, poor structural stability, and sluggish ion/electron diffusion kinetics remain the obstacles that have to be overcome. Here, we report the synthesis of a few-layered two-dimensional covalent organic framework trapped by carbon nanotubes as the anode of lithium-ion batteries. Remarkably, upon activation, this organic electrode delivers a large reversible capacity of 1536 mAh g-1 and can sustain 500 cycles at 100 mA g-1. Aided by theoretical calculations and electrochemical probing of the electrochemical behavior at different stages of cycling, the storage mechanism is revealed to be governed by 14-electron redox chemistry for a covalent organic framework monomer with one lithium ion per C=N group and six lithium ions per benzene ring. This work may pave the way to the development of high-capacity electrodes for organic rechargeable batteries.