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.