Chirality-selected single-walled carbon nanotubes (SWCNTs) ensure a great potential of building ~1 nm sized electronics. However, the reliable method for chirality-selected SWCNT is still pending. Here we present a theoretical study on the SWCNTs chirality assignment and control during the catalytic growth. This study reveals that the chirality of a SWCNT is determined by the kinetic incorporation of the pentagon formation during SWCNT nucleation. Therefore, chirality is randomly assigned on a liquid catalyst surface. Furthermore, based on the understanding, two potential methods of synthesizing chirality-selected SWCNTs are proposed: i) by using Ta, W, Re, Os, or their alloys as solid catalysts, and ii) by changing the SWCNTs chirality frequently during the growth.