In this paper, we report the design of numerous models of CsCn- (n = 1-10). By means of B3LYP density functional method, we carried out geometry optimization and calculation on the vibrational frequency. We found that the CsCn- (n = 4-10) clusters with Cs lightly embraced by C-n are ground-state isomers. The structures are composed of C-n(2-) and Cs+ with the former being electronically stabilized by the latter. When n is even, the C-n (n = 4-10) chain is polyacetylene-like. The CSCn- (n = 1-10) with even n are found to be more stable than those with odd n, and the result is in accord with the relative intensities of CsCn- (n = 1-10) observed in mass spectrometric studies. In this paper, we provide explanations for such trend of even/odd alternation based on concepts of the highest vibrational frequency, incremental binding energy, electron affinity, and dissociation channels.