In this work, we report results of calculations, based on density functional theory (DFT/B3LYP/6-311G*), of the lowest state energies, electronic structures, dipole moments, and vibrational frequencies of CnP, CnP+, and CnP- (n = 1-7) clusters. According to these calculations, the lowest-lying geometry of all these species is predicted to be a linear structure with phosphorus located at one end of the carbon chain. From various theoretical considerations, such as incremental binding energy diagrams and fragmentation patterns, we can deduce that anionic clusters, CnP-, with odd clustering atoms are much more stable than those with even clustering atoms, in good agreement with experimental results (odd-even parity). Similar predictions can be made for the neutrals, although the odd-even alternation in stability is much less marked in this case. Besides, cations CnP+ exhibit an even-odd parity effect completely opposite to that of CnP- and CnP.