By combining in situ annealing and Raman spectroscopy measurements, the growth dynamics of nine individual-chirality inner tubes (8,8), (12,3), (13,1), (9,6), (10,4), (11,2), (11,1), (9,3) and (9,2) with diameters from ~0.8 to 1.1 nm are monitored using a time resolution of several minutes. The growth mechanism of inner tubes implies two successive stages of the growth on the carburized and purely metallic catalytic particles, respectively, which are formed as a result of the thermally induced decomposition of metallocenes inside the outer SWCNTs. The activation energies of the growth on carburized Ni and Co catalytic particles amount to 1.85–2.57 eV and 1.80–2.71 eV, respectively. They decrease monotonically as the tube diameter decreases, independent of the metal type. The activation energies of the growth on purely metallic Ni and Co particles equal 1.49–1.91 eV and 0.77–1.79 eV, respectively. They increase as the tube diameter decreases. The activation energies of the growth of large-diameter tubes (dt = ~0.95–1.10 nm) on Ni catalyst are significantly larger than on Co catalyst, whereas the values of small-diameter tubes (dt = ~0.80–0.95 nm) are similar. For both metals, no dependence of the activation energies on the chirality of inner tubes is observed.