Imine, hydrazone, and olefin-linked covalent organic frameworks (COFs) prosper in visible light photocatalysis. Markedly, the olefin-linked COFs are usually superior in transfer of π-conjugated electron powered by visible light albeit their construction is more challenging. Herein, two olefin-linked COFs were forged between 2,4,6-trimethyl-1,3,5-triazine (TMT) and 2,4,6-tris(4-formyl-phenyl)-1,3,5-triazine (TFPT) or 1,3,5-tris(4-formyl-phenyl)-benzene (TFPB) to afford TTO-COF or TBO-COF, respectively. Both of the olefin-linked COFs based on triazine are of good crystallinity, uniform micropores, and high specific surface areas, but of different morphologies, namely nanotubes and nanosheets. Compared to TBO-COF, TTO-COF nanotubes were constructed with two building blocks based on triazine, which could not only improve the planarity of a single layer but also cause closer stacking of layers in between. Therefore, TTO-COF nanotubes exhibit better photocatalytic performance and stability in the selective oxidation of organic sulfides into corresponding sulfoxides with O₂ powered by blue light. Mechanistic investigation evidence the formation of desired sulfoxides was shaped by both electron and energy transfer pathways over TTO-COF nanotubes. This work underlines the ascendancy of olefin-linked COFs inasmuch as they provide an effective platform to construct efficient and durable photocatalysts based on adaptable organic building blocks.