The growth kinetics of single-walled carbon nanotubes (SWCNTs) in a low-temperature, low-pressure reactive plasma is investigated using a multiscale numerical simulation, including the plasma sheath and surface diffusion modules. The plasma-related effects on the characteristics of SWCNT growth are studied. It is found that in the presence of reactive radicals in addition to energetic ions inside the plasma sheath area, the effective carbon flux, and the growth rate of SWCNT increase. It is shown that the concentration of atomic hydrogen and hydrocarbon radicals in the plasma plays an important role in the SWCNT growth. The effect of the effective carbon flux on the SWCNT growth rate is quantified. The dependence of the growth parameters on the substrate temperature is also investigated. The effects of the plasma sheath parameters on the growth parameters are different in low- and high-substrate temperature regimes. The optimum substrate temperature and applied DC bias are estimated to maximize the growth rate of the single-walled carbon nanotubes.