The core electron binding energies (CEBEs) and core-level excitation energies of thymine, adenine, cytosine, and uracil are studied by the Kohn-Sham (KS) method with long-range corrected (LC) functionals. The CEBEs are estimated according to the Koopmans-type theorem for density functional theory. The excitation energies from the core to the valence pi* and Rydberg states are calculated as the orbital energy differences between core-level orbitals of a neutral parent/cation and unoccupied pi* or Rydberg orbitals of its cation. The model is intuitive, and the spectra can easily be assigned. Core excitation energies from oxygen Is, nitrogen Is, and carbon is to pi* and Rydberg states, and the chemical shifts, agree well with previously reported theoretical and experimental data. The straightforward use of KS orbitals in this scheme carries the advantage that it can be applied efficiently to large systems such as biomolecules and nanomaterials.