Although the growth of single-wall carbon nanotubes (SWCNTs) with a chirality selectivity up to 90% has been successfully achieved using solid catalysts ( Yang , F. Nature , 2014 , 510 , 522 ; Zhang , S. ; Nature , 2017 , 543 , 234 , etc.), the underlying mechanism that governs the chirality selection is far from clear. Here we propose a mechanism to understand how a solid catalyst particle determines the structure of the SWCNT grown on it. The mechanism has to satisfy three criteria: (i) thermodynamic selection of SWCNTs that possess a structural symmetry the same as that of the catalyst surface; (ii) kinetic elimination of the achiral SWCNTs with extremely low growth rates; (iii) rough control over the catalyst particle size leads to SWCNTs with only one or a few dominant chiralities. Besides the deep understanding on the mechanisms of experimentally synthesized (12, 6) and (8, 4) SWCNTs, the preference growth of other SWCNTs of the (2 n, n) family, such as the (10, 5) or (6, 3) SWCNTs, by using catalyst surface with a 5- or 3-fold symmetry is predicted. Such a simple three-criteria mechanism deepens our understanding of the selective growth of SWCNTs and provides a guideline for catalyst design for controlled SWCNT synthesis.