A comparative investigation has been carried out on second-row-atom-doped linear carbon clusters CnX/CnX+/CnX- (n = 1-10) using density functional theory (DFT-B3LYP) method in conjunction with 6-311+G* basis sets. For each linear CnX/CnX+/CnX- species, the low-lying states, total energies, geometries, incremental binding energies, ionization potentials, and electron affinities are considered. The incremental binding energy diagrams show that, doped by different heteroatoms X, CnX/CnX+/CnX- clusters exhibit different parity alternation effects in their stabilities, and these parity effects also appear in the ionization potential and electron affinity curves. For different kinds of the CnX/CnX+/CnX- clusters, the parity effects in their stabilities are discussed and compared. Systematic investigations of their electronic distributions find that the parity effects in their stabilities are attributed to the numbers of their valence 7-electrons.