The intermetallic Co7W6 catalysts have shown great success in chirality-specified growth of single-walled carbon nanotubes (SWCNTs). Electron microscopic techniques, particularly the in-situ techniques enable us to study the growth mechanism and the behavior of catalysts at atomic scale. It was found that the structure of Co7W6 nanocrystals were stable at the temperature of 1100 °C under carbon feeding condition. No carbon dispersion within the nanocrystal happened. These observations illustrate why such kind of catalysts can act as the structural template to grow SWCNTs with specified chiralities. Due to the less efficient carbon diffusion and supply on the surface of catalysts in such a vapor-solid-solid process than that in a vapor-liquid-solid process, SWCNTs normally nucleate on larger catalyst nanocrystals. All these behaviors are distinctly different from those of normal metallic catalysts, demonstrating the uniqueness of intermetallic Co7W6 catalysts in chirality-selective growth of SWCNTs. These results can help us to further understand the mechanism of the origination of chirality selectivity in SWCNT growth, benefiting the rational design of catalysts.