The development of efficient photocatalysts to convert low-concentration CO2 into the value-added chemicals and fuels is particularly interesting yet remains highly challenging. Herein, we designed and synthesized three metal-covalent organic frameworks (MCOFs) through the Schiff-base condensation reactions between trinuclear copper complex and different BDP-based chromophores (BDP = 4,4-difluoro-4-bora-3a,4a-diaza-s-indacene) for visible-light-driven reduction of low-concentration CO2 (15%) to HCOO-. As a result, MCOF-ANT containing anthracene (ANT) groups achieves the highest HCOO- production rate of 1658 mu mol g(-1) h(-1) (HCOO- selectivity, similar to 100%) in the absence of any additional noble-metal photosensitizers under a laboratory light source, which is 7.2 and 2.1 times higher than those of MCOF-Ph and MCOF-Nap with phenyl (Ph) and naphthalene (Nap) groups, respectively. Furthermore, MCOF-ANT also exhibits excellent photocatalytic activity for the reduction of low-concentration CO2 (15%) to HCOO- under natural sunlight, with a HCOO- production rate of 1239 mu mol g(-1) h(-1) (HCOO- selectivity, similar to 100%). Experiments and theoretical calculations reveal that the presence of ANT in MCOF-ANT is favorable to the visible-light harvesting and charge separation, as well as the formation of *OCO intermediate, which clearly accounts for its superior catalytic activity.