Abstract: The energetic of the change in the chirality of single-wall carbon nanotubes (SWCNTs)during epitaxial growth from (n, m) to (n±Δ, m Δ)(Δ=1, 2) was investigated by density functional theory calculations. The calculated energies for changing the chirality of different SWCNTs show a nearly linear decrease with decreasing tube diameter. In the case of Δ=1, more energy input is needed for near armchair (nAC) SWCNTs to change their chiralities than those for near zigzag (nZZ) SWCNTs with comparable diameters, due to the larger formation energies of pentagon-heptagon defects (5,7-defects) introduced in the nAC-SWCNTs. These larger formation energies for the nAC-SWCNTs come from the larger angles between the orientation of a 5,7-defect and the tube axis than those for nZZ-SWCNTs. The topological connection oftwo adjacent 5,7-defects, which is indispensable for changing the chirality during growth in the case of Δ=2, is found to be energetically most stable. The energies needed to change chirality in the case of Δ=2 are calculated to be less than twice those in the case of Δ=1 for SWCNTs with comparable diameters. These results may help us understand the change in chirality during the epitaxial growth of SWCNTs and guide the future synthesis of SWCNTs with a single-chirality.