Semiconducting single-walled carbon nanotubes (SWNTs) with controlled chirality (n, m) and band gaps are expected to create a new era of electronics. Here, we report a rational design to enable SWNTs' near-equilibrium nucleation and then grow a new family of semiconducting SWNTs: (n, n - 1) carbon nano-tubes. No metallic SWNTs were observed in similar to 100 samples by reflection optical spectral measurements. Combined with catalyst controlling, we have successfully synthesized both large-diameter (>2 nm) (n, n - 1) SWNTs and single-chirality (10, 9) SWNTs with abundances of 88% and >80%, respectively. Theoretical analysis indicates that the chirality of (n, n) tubes tends to change to (n, n - 1) by kinetically incorporating an energetically preferred pentagon-heptagon pair in the tube wall. This strategy opens up a new route for the growth of SWNT families beyond catalyst design.