Multireference configuration interaction calculations on the vertical transition energies of the low-lying excited states in carbon chain anions C-2n+1(-) (n=2-5) are carried out. Calculated vertical term energies confirm the previously suggested assignments to the first and second (2)Pi <--X (2)Pi band systems in matrix isolation spectroscopy. The lowest 1 (2)Pi <--X (2)Pi electronic transitions of C-5(-), C-7(-), C-9(-), and C-11(-), are calculated at 2.66, 2.27, 1.90, and 1.54 eV, respectively, with large oscillator strengths. Relevant theoretical evidences for a more detailed assignment of the observed transitions are presented. Generally, corresponding excitation energies in the C-2n+1(-) carbon chain anions are found descending with an increase of the chain. The equilibrium geometries and harmonic vibrational frequencies of these linear carbon chains determined by the density functional theory approach also show reasonable agreement with available experimental data.