Understanding the nucleation and growth process of carbon nanotubes (CNTs) is important for guiding their efficient and controllable synthesis in industry. However, the intrinsic mechanism that controls the formation of carbon nanotubes is still controversial. Here, using in-situ transmission electron microscopy (TEM), we demonstrate the dynamic catalytic growth of multilayered graphite crystallites and single-walled carbon nanotubes (SWCNTs) from the Co2C catalyst nanoparticles (NPs) at the atomic resolution. The dissociative carbon atoms arrive at the nucleation sites on the surface of small and large NPs by the surface and bulk diffusion, respectively. These two different diffusion modes are found to be the essential prerequisite for growing single-walled carbon nanotubes (SWCNTs) or multilayered graphite crystallites. The small NPs utilize crystal self-rotation to expose the (111) plane for efficiently capturing carbon atoms, while the large NPs use self-reshaping on (111) facets to provide atomic steps as active nucleation sites. Density functional theory (DFT) calculations indicate that the observations are in good agreement with the growth mechanism of graphite structures involving the preferential selectivity of crystal facets. Our results may open up the possibility of adjusting the size and crystal orientation of cobalt-based catalyst particles to efficiently synthesize the SWCNTs with high quality.