The potential energy curves (PECs) of 24 Lambda-S states and 54 Omega states of the C-2(+) cation are studied in detail using an ab initio quantum chemical method. All the PEC calculations are made for internuclear separations from 0.09 to 1.11 nm by the complete active space self-consistent field method, which is followed by the internally contracted multireference configuration interaction approach with the Davidson modification (MRCI+Q). All the Lambda-S states involved dissociate into the first dissociation limit, C(P-3(g)) + C+(P-2(u)), of C-2(+) cation, of which only the 2(2)Sigma(-)(g) and 2(4)Sigma(-)(g) are repulsive. The spin-orbit (SO) coupling effect is accounted for by the Breit-Pauli Hamiltonian with an aug-cc-pCVTZ basis set. To improve the quality of PECs, core-valence correlation and scalar relativistic corrections are included. Core-valence correlation corrections are taken into account with an aug-cc-pCVTZ basis set. Scalar relativistic correction calculations are done by the third-order Douglas-Kroll Hamiltonian approximation with the cc-pVQZ basis set. All the PECs are extrapolated to the complete basis set limit. The convergence observations of present calculations are made, and the convergent behavior is discussed with respect to the basis set and level of theory. With the PECs obtained by the MRCI+WCV+DK+56 calculations, the spectroscopic parameters of 22 Lambda-S bound states of C-2(+) cation are evaluated by fitting the first ten vibrational levels, which are obtained by solving the rovibrational Schrodinger equation using Numerov's method. In addition, the spectroscopic parameters of 51 Omega bound states generated from these Lambda-S bound states are also obtained. The spectroscopic parameters are compared with those reported in the literature. Excellent agreement with available measurements is found. It is expected that the spectroscopic parameters of Lambda-S and Omega states reported here are reliable predicted ones.