Covalent organic frameworks (COFs) have emerged as promising photocatalysts for hydrogen peroxide (H₂O₂) production, yet their performance is often limited by inefficient photogenerated charge separation and transport. Herein, a sp² carbon-conjugated donor-acceptor-acceptor (D-A-A) COF (TFPT-TCPB-COF) incorporating a strong electron-withdrawing cyano group was rationally designed and synthesized via an optimized solvothermal method. The unique D-A-A architecture, together with abundant reductive active sites (triazine and cyano groups) for two-electron oxygen reduction and oxidative sites (benzene rings) for two-electron water oxidation, enables efficient H₂O₂ generation in pure water without sacrificial agents. As a result, TFPT-TCPB-COF achieves a high H₂O₂ production rate of 4.43 mmol g^-1 h^-1, which is 1.72 times greater than that of its imine-linked analogue (TFPT-TAPB-COF). Additionally, it exhibits an apparent quantum yield of 12.4% at 420 nm, outperforming most reported COF-based photocatalysts. Experimental and theoretical analyses reveal that the enhanced activity originates from improved charge separation and transport, as well as a modulated electronic structure that lowers the energy barriers for key *OOH and *OH intermediates during the photocatalytic process. This work provides important molecular insights into the design of advanced COF photocatalysts with donor-acceptor architectures for efficient solar energy conversion.