The BP86 DFT, CCSD(T), and CASPT2 methods were employed to study the low-lying states of NbC3-/0 clusters. The anionic and neutral ground states were determined to be the 'A, and 1(2)A(1) of the cyclic-NbC3-/0 isomers. All bands in the photoelectron spectra of the NbC3- cluster were interpreted based on electron detachment processes from the (1)A(1) of the cyclic-NbC3- isomer. The X, A, B, and C bands in the spectra are, respectively, ascribed to the transitions from (1)A(1) to the 1(2)A(1), B-2(1), 2(2)A(1), and B-2(2) states. The wave function of the initial (1)A(1) anionic state exhibits a pronounced multireference character that plays to some extent a role in the (1)A(1) -> I(2)A(1) and the (1)A(1) -> 2(2)A(1) ionizations. Only the (1)A(1) -> B-2(2) transition appears as a clear one-electron detachment process. The Franck-Condon factor simulations for the (1)A(1) -> 1(2)A(1) and (1)A(1) -> B-2(1) transitions are consistent with the observed vibrational progressions of the X and A bands in the spectra.