Geometries of 10, 7, and 6 low-lying states of the HCCN neutral radical, its anion and cation, were optimized by using the complete active space self-consistent field (CASSCF) method in conjunction with the aug-cc-pVTZ basis set, respectively. Taking the further correlation effects into account, the second-order perturbations (CASPT2) were carried out for the energetic correction. Vertical excitation energies (T-v) at the ground state geometry of the HCCN neutral radical were calculated for 11 states. The results of our calculations suggest that the spin-allowed transitions of HCCN at 4.179, 4.395, 4.579, 4.727 and 5.506 eV can be attributed to X(3)A" -> 2(3)A", X(3)A" -> (3)A', X(3)A -> 3(3)A", X(3)A" -> 2(3)A', and X(3)A" -> 3(3)A', respectively. The singlet-triplet splitting gap of HCCN is calculated to be 0.738 eV. The vertical and adiabatic ionization energies were obtained to compare with the PES data. The results we obtained were consistent with the available experiment results.