Olefin-linked covalent organic frameworks (COFs) have exhibited great potential in visible-light photocatalysis. In principle, expanding fully conjugated COFs can facilitate light absorption and charge transfer, leading to improved photocatalysis. Herein, three olefin-linked COFs with the same topology are synthesized by combining 2,4,6-trimethyl-1,3,5-triazine (TMT) with 1,3,5-triformylbenzene (TFB), 1,3,5-tris(4-formylphenyl)benzene (TFPB), and 1,3,5-tris(4-formylphenylethynyl)benzene (TFPEB), namely, TMT-TFB-COF, TMT-TFPB-COF, and TMT-TFPEB-COF, respectively. From TMT-TFB-COF to TMT-TFPB-COF, expanding phenyl rings provides only limited expansion for π-conjugation due to the steric effect of structural twisting. However, from TMT-TFPB-COF to TMT-TFPEB-COF, the insertion of acetylenes eliminates the steric effect and provides more delocalized π-electrons. As such, TMT-TFPEB-COF exhibits the best optoelectronic properties among these three olefin-linked COFs. Consequently, the photocatalytic performance of TMT-TFPEB-COF is much better than those of TMT-TFB-COF and TMT-TFPB-COF on the oxidation of organic sulfides into sulfoxides with oxygen. The desirable reusability and substrate compatibility of the TMT-TFPEB-COF photocatalyst are further confirmed. The selective formation of organic sulfoxides over TMT-TFPEB-COF under blue light irradiation proceeds via both electron- and energy-transfer pathways. This work highlights a rational design of expanding the π-conjugation of fully conjugated COFs toward selective visible-light photocatalysis.