Photocatalytic water splitting is a promising solution to sustainable hydrogen production. Recently, conjugated covalent organic frameworks (COFs) with highly designable skeleton and inherent pores have emerged as promising photocatalysts for water splitting. However, structure-property relationships in COFs have not been established and the rational design of COFs with suitable electronic properties and chemical structures for water splitting is challenging. In this work, we proposed a facile strategy that is based on tailoring donor (D) and acceptor (A) building blocks of COFs in Lieb lattice, to achieve visible light absorption, prompt exciton dissociation, and metal-free hydrogen evolution. We constructed eight fully conjugated D-A COFs with a pyrene donor node and different acceptor edges linked by C=C and demonstrated that as compared to the D-D COF, D-A design not only shifted optical absorption to the visible and near-infrared region, but also modified band alignment to trigger overall water splitting. Moreover, the charge-transfer excitation in D-A COFs produced space-separated electrons and holes, and the exciton binding energy was substantially reduced due to increased dielectric screening in D-A COFs. Further, we found that the overpotential for hydrogen evolution reaction was suppressed by introducing hydrogen bond interactions in the hydrogen adsorption intermediate to enable metal-free catalysis. Finally, we attained five D-A COFs capable of visible-light-driven hydrogen production in neutral solution without the load of metal co-catalysts. These findings highlight a new route to design COF-photocatalysts and offer tremendous opportunities for regulating COFs towards efficient photocatalytic water splitting and other chemical transformations.