  Doubly ionized cerium (Ce$^{2+}$) is one of the most important ions to
understand the kilonova spectra. In particular, near-infrared (NIR) transitions
of Ce III between the ground (5p$^6$ 4f$^2$) and first excited (5p$^6$ 4f 5d)
configurations are responsible for the absorption features around 14,500 A.
However, there is no dedicated theoretical studies to provide accurate
transition probabilities for these transitions. We present energy levels of the
ground and first excited configurations and transition data between them for Ce
III. Calculations are performed using the GRASP2018 package, which is based on
the multiconfiguration Dirac-Hartree-Fock and relativistic configuration
interaction methods. Compared with the energy levels in the NIST database, our
calculations reach the accuracy with the root-mean-square (rms) of 2732
cm$^{-1}$ or 1404 cm$^{-1}$ (excluding one highest level) for ground
configuration, and rms of 618 cm$^{-1}$ for the first excited configuration. We
extensively study the line strengths and find that the Babushkin gauge provide
the more accurate values. By using the calculated gf values, we show that the
NIR spectral features of kilonova can be explained by the Ce III lines.
