The C-C bond lengths of the linear magnetic neutral CnSb, CnSb+ cations and CnSb− anions are within 1.255–1.336 Å, which is typical for cumulene structures with moderately strong double-bonds. In this report, we found that the adiabatic ionization energy (IE) of CnSb decreased with n. When comparing the IE~n relationship of CnSb with that of pure Cn, we found that the latter exhibited a stair-step pattern (n ≥ 6), but the IE~n relationship of CnSb chains took the shape of a flat curve. The IEs of CnSb were lower than those of corresponding pure carbon chains. Different from pure carbon chains, the adiabatic electron affinity of CnSb does not exhibit a parity effect. There is an even-odd alternation for the incremental binding energies of the open chain CnSb (for n = 1–16) and CnSb+ (n = 1–10, when n > 10, the incremental binding energies of odd (n) chain of CnSb+ are larger than adjacent clusters). The difference in the incremental binding energies between the even and odd chains of both CnSb and pure Cn diminishes with the increase in n. The incremental binding energies for CnSb- anions do not exhibit a parity effect. For carbon chain clusters, the most favorable binding site of atomic antimony is the terminal carbon of the carbon cluster because the terminal carbon with a large spin density bonds in an unsaturated way. The C-Sb bond is a double bond with Wiberg bond index (WBI) between 1.41 and 2.13, which is obviously stronger for a carbon chain cluster with odd-number carbon atoms. The WBI of all C-C bonds was determined to be between 1.63 and 2.01, indicating the cumulene character of the carbon chain. Generally, the alteration of WBI and, in particular, the carbon chain cluster is consistent with the bond length alteration. However, the shorter C-C distance did not indicate a larger WBI. Rather than relying on the empirical comparison of bond distance, the WBI is a meaningful quantitative indicator for predicting the bonding strength in the carbon chain.