Depending on its specific structure, or so-called chirality, a single-walled carbon nanotube (SWCNT) can be either a conductor or a semiconductor. This feature ensures great potential for building ∼1 nm sized electronics if chirality-selected SWCNTs could be achieved. However, due to the limited understanding of the growth mechanism of SWCNTs, reliable methods for chirality-selected SWCNTs are still pending. Here we present a theoretical model on the chirality assignment and control of SWCNTs during the catalytic growth. This study reveals that the chirality of a SWCNT is determined by the kinetic incorporation of pentagons, especially the last (6th) one, during the nucleation stage. Our analysis showed that the chirality of a SWCNT is randomly assigned on a liquid or liquid-like catalyst surface, and two routes of synthesizing chirality-selected SWCNTs, which are verified by recent experimental achievements, are demonstrated. They are (i) by using high melting point crystalline catalysts, such as Ta, W, Re, Os, or their alloys, and (ii) by frequently changing the chirality of SWCNTs during their growth. This study paves the way for achieving chirality-selective SWCNT growth for high performance SWCNT based electronics.