Covalent organic frameworks (COFs) nanostructures capable of efficient visible light absorption, complete holes-electrons separation, and reactant enrichment remain a synthetic challenge for advanced photocatalysts. Herein, we rationally design a novel Cu-coordinated terpyridyl-based, 2D lamellar COF-909(Cu) nanorods. The coordinated single Cu sites not only dramatically enhance the visible light absorption and achieve the complete electrons-holes separation, but also provide the specific binding sites to enrich N/O-containing organic toxicants. The laminar arrangement and 1D nanochannel of COF-909(Cu) nanorods shorten the transfer distance of electrons to the active sites. As a proof of concept, it shows excellent performance in the photocatalytic degradation of sulfamethoxazole, which surpasses the-state-of-art photocatalysts. Density functional theory calculations confirm the structure-function relationship between the single Cu sites and the complete electrons-holes separation as well as strong binding sites for target molecules.