Two-dimensional (2D) covalent organic frameworks (COFs) are promising metal-free materials for photocatalytic water splitting because of their high surface area and predictability to assemble various molecules with tunable electronic properties. Unfortunately, 2D COFs capable of visiblelight-driven photocatalytic overall water splitting are rare, partly due to rigorous requirements to their band alignments and coexistence of catalytic sites for both hydrogen evolution reaction (HER) and oxygen evolution reaction (OER). Herein, 12 2D nitrogen-linked COFs are designed based on first-principles calculations and topological assembly of molecular segments with catalytic activities toward either HER or OER, respectively. The electronic band structures calculated with HSE06 method indicate that 2D COFs are semiconductors with a widely tunable bandgap ranging from 1.92 to 3.23 eV. The positions of both conduction and valence band edges of nine 2D COFs match well with the chemical reaction potential of H-2/H+ and O-2/H2O, which are capable of photocatalytic overall water splitting. Of particular importance is that three of them based on 2,4,6-tris(4-methylphenyl)-1,3,5-triazine (TST) can split water into hydrogen and oxygen under visible light. Our results agree with respect to the literature, with three of them having been studied for photocatalytic HER or CO2 reduction. In addition, we further experimentally demonstrate that I-TST presents both HER and OER activity under visible light. Our findings present a route to design practical 2D COFs as metal-free and single-material photocatalysts for overall water splitting under visible light.