High-melting point alloy catalysts have been reported to be effective for the structure-controlled growth of single-wall carbon nanotubes (SWCNTs). However, some fundamental issues remain unclear because of the complex catalytic growth environment. Here, we directly investigated the active catalytic phase of Co-W-C alloy catalyst, the growth kinetics of CNTs, and their interfacial dynamics using closed-cell environmental transmission electron microscopy at atmospheric pressure. The alloy catalyst was precisely identified as a cubic η-carbide phase that remained unchanged during the whole CNT growth process. Rotations of the catalyst nanoparticles during CNT growth were observed, implying a weak interfacial interaction and undefined orientation dependence for the solid catalyst. Theoretical calculations suggested that the growth kinetics are determined by the diffusion of carbon atoms on the surface of the η-carbide catalyst and through the interface of the catalyst-CNT wall.