A DFT theoretical study of the CaCn, CaCn+, CaCn- (n = 1-8) open-chain clusters has been carried out using the B3LYP method with both 6-311G(d) and 6-311+G(d) basis sets. For each species several molecular properties such as vibrational frequencies, dipole moments, and rotational constants are reported. For the CaCn open-chain clusters the lowest-lying states correspond to triplet states for n-odd members, whereas in the n-even species the ground states were found to be singlets. Cationic clusters have doublet ground states with the exception of the smallest one, CaC+. In CaCn- clusters, except for CaC3-, the ground state is alternate between quartets (for n-odd members) and doublets (for n-even members). The incremental binding energy diagrams show a clear odd-even alternation in the cluster stability in both neutral and anionic clusters with their n-even members being more stable than the corresponding n-odd ones, while the parity effects is less pronounced for the cationic clusters. This odd-even alternation was also found for the electron affinities, whereas there is not a clear alternation in the ionization potentials.