Carbon-based single-atom catalysts (SACs) for electrochemical nitrogen reduction reaction (NRR) have received increasing attention due to their sustainable, efficient, and green advantages. However, at present, the research on carbon nanotubes (CNTs)-based NRR catalysts is very limited. In this paper, using FeN3@(n, 0) CNTs (n = 3 ~ 10) as the representative catalysts, we demonstrate that the CNT curvatures will affect the spin polarization of the catalytic active centers, the activation of the adsorbed N2molecules and the Gibbs free energy barriers for the formation of the critical intermediates in the NRR processes, thus changing the catalytic performance of CNT-based catalysts. Zigzag (8, 0) CNT was taken as the optimal substrate, and twenty transition metal atoms (Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Nb, Mo, Tc, Ru, Rh, Pd, W, Re, Ir, and Pt) were embedded into (8, 0) CNT via N3group to construct the NRR catalysts. Their electrocatalytic performance for NRR were examined using DFT calculations, and TcN3@(8, 0) CNT was screened out as the best candidate with a low onset potential of − 0.53 V via the distal mechanism, which is superior to the molecules- or graphene-support Tc catalysts. Further electronic properties analysis shows that the high NRR performance of TcN3@(8, 0) CNT originates from the strongd-2π* interaction between the N2molecule and Tc atom. TcN3@(8, 0) CNT also exhibits higher selectivity for NRR than the competing hydrogen evolution reaction (HER) process. The present work not only provides a promising catalyst for NRR, but also open up opportunities for further exploring of low-dimensional carbon-based high efficiency electrochemical NRR catalysts.