  A microscopic method for calculating nuclear level density (NLD) based on the
covariant density functional theory (CDFT) is developed. The particle-hole
state density is calculated by combinatorial method using the single-particle
levels schemes obtained from the CDFT. Then the level densities are obtained by
taking into account collective effects such as vibration and rotation. Our
results are compared with those from other NLD models, including
phenomenological, microstatistical, and non-relativistic HFB combinatorial
models. The comparison suggests that the general trends among these models are
basically the same, except for some deviations from different NLD models. In
addition, the NLDs of the CDFT combinatorial method with normalization are
compared with experimental data, including the observed cumulative number of
levels at low excitation energy and the measured NLDs. Compared with the
existing experimental data, the CDFT combinatorial method can give reasonable
results.
