An understanding of the growth mechanism of carbon nanotubes (CNTs) is very important for the control of their structures, which in turn will be the basis for their further theoretical studies and applications. On the basis of high-resolution transmission electron microscopy observations of the initial nucleation of CNTs, the following deductions are made: (1) the nucleation of single-walled carbon nanotubes (SWNTs) and double-walled carbon nanotubes (DWNTs) starts at a low-temperature zone in front of the reaction zone; (2) the addition of sulfur results in localized liquid zones on the surface of big catalyst particles as the initial nucleation sites; (3) a temperature gradient is necessary to realize the role of sulfur in the structure of CNTs; and (4) the shell number of CNTs can be changed at the nucleation and growth stages. On the basis of the above, a growth model for the formation of SWNTs and DWNTs is proposed, which might open up the possibility of controlling the structure of CNTs.